Daily Papers

In this paper, we propose to use deep policy networks which are trained with an advantage actor-critic method for statistically optimised dialogue systems. First, we show that, on summary state and action spaces, deep Reinforcement Learning (RL) outperforms Gaussian Processes methods. Summary state and action spaces lead to good performance but require pre-engineering effort, RL knowledge, and domain expertise. In order to remove the need to define such summary spaces, we show that deep RL can also be trained efficiently on the original state and action spaces. Dialogue systems based on partially observable Markov decision processes are known to require many dialogues to train, which makes them unappealing for practical deployment. We show that a deep RL method based on an actor-critic architecture can exploit a small amount of data very efficiently. Indeed, with only a few hundred dialogues collected with a handcrafted policy, the actor-critic deep learner is considerably bootstrapped from a combination of supervised and batch RL. In addition, convergence to an optimal policy is significantly sped up compared to other deep RL methods initialized on the data with batch RL. All experiments are performed on a restaurant domain derived from the Dialogue State Tracking Challenge 2 (DSTC2) dataset.

Quantum computing offers efficient encapsulation of high-dimensional states. In this work, we propose a novel quantum reinforcement learning approach that combines the Advantage Actor-Critic algorithm with variational quantum circuits by substituting parts of the classical components. This approach addresses reinforcement learning's scalability concerns while maintaining high performance. We empirically test multiple quantum Advantage Actor-Critic configurations with the well known Cart Pole environment to evaluate our approach in control tasks with continuous state spaces. Our results indicate that the hybrid strategy of using either a quantum actor or quantum critic with classical post-processing yields a substantial performance increase compared to pure classical and pure quantum variants with similar parameter counts. They further reveal the limits of current quantum approaches due to the hardware constraints of noisy intermediate-scale quantum computers, suggesting further research to scale hybrid approaches for larger and more complex control tasks.

Effective offline RL methods require properly handling out-of-distribution actions. Implicit Q-learning (IQL) addresses this by training a Q-function using only dataset actions through a modified Bellman backup. However, it is unclear which policy actually attains the values represented by this implicitly trained Q-function. In this paper, we reinterpret IQL as an actor-critic method by generalizing the critic objective and connecting it to a behavior-regularized implicit actor. This generalization shows how the induced actor balances reward maximization and divergence from the behavior policy, with the specific loss choice determining the nature of this tradeoff. Notably, this actor can exhibit complex and multimodal characteristics, suggesting issues with the conditional Gaussian actor fit with advantage weighted regression (AWR) used in prior methods. Instead, we propose using samples from a diffusion parameterized behavior policy and weights computed from the critic to then importance sampled our intended policy. We introduce Implicit Diffusion Q-learning (IDQL), combining our general IQL critic with the policy extraction method. IDQL maintains the ease of implementation of IQL while outperforming prior offline RL methods and demonstrating robustness to hyperparameters. Code is available at https://github.com/philippe-eecs/IDQL.

Credit assignment is a central challenge in reinforcement learning (RL). Classical actor-critic methods address this challenge through fine-grained advantage estimation based on a learned value function. However, learned value models are often avoided in modern large language model (LLM) RL because conventional discriminative critics are difficult to train reliably. We revisit value modeling and argue that this difficulty is partly due to limited expressiveness. In particular, representation complexity theory suggests that value functions can be hard to approximate under the one-shot prediction paradigm used by existing value models, and our scaling experiments show that such critics do not improve reliably with scale. Motivated by this observation, we propose Generative Actor-Critic (GenAC), which replaces one-shot scalar value prediction with a generative critic that performs chain-of-thought reasoning before producing a value estimate. We further introduce In-Context Conditioning, which helps the critic remain calibrated to the current actor throughout training. GenAC improves value approximation, ranking reliability, and out-of-distribution generalization, and these gains translate into stronger downstream RL performance than both value-based and value-free baselines. Overall, our results suggest that stronger value modeling is a promising direction for improving credit assignment in LLM reinforcement learning.

The role of reinforcement learning (RL) in enhancing the reasoning of large language models (LLMs) is becoming increasingly significant. Despite the success of RL in many scenarios, there are still many challenges in improving the reasoning of LLMs. One challenge is the sparse reward, which makes optimization difficult for RL and necessitates a large amount of data samples. Another challenge stems from the inherent instability of RL, particularly when using Actor-Critic (AC) methods to derive optimal policies, which often leads to unstable training processes. To address these issues, we introduce Direct Advantage Policy Optimization (DAPO), an novel step-level offline RL algorithm. Unlike standard alignment that rely solely outcome rewards to optimize policies (such as DPO), DAPO employs a critic function to predict the reasoning accuracy at each step, thereby generating dense signals to refine the generation strategy. Additionally, the Actor and Critic components in DAPO are trained independently, avoiding the co-training instability observed in standard AC algorithms like PPO. We train DAPO on mathematical and code query datasets and then evaluate its performance on multiple benchmarks. Our results show that DAPO can effectively enhance the mathematical and code capabilities on both SFT models and RL models, demonstrating the effectiveness of DAPO.

The wide popularity of short videos on social media poses new opportunities and challenges to optimize recommender systems on the video-sharing platforms. Users sequentially interact with the system and provide complex and multi-faceted responses, including watch time and various types of interactions with multiple videos. One the one hand, the platforms aims at optimizing the users' cumulative watch time (main goal) in long term, which can be effectively optimized by Reinforcement Learning. On the other hand, the platforms also needs to satisfy the constraint of accommodating the responses of multiple user interactions (auxiliary goals) such like, follow, share etc. In this paper, we formulate the problem of short video recommendation as a Constrained Markov Decision Process (CMDP). We find that traditional constrained reinforcement learning algorithms can not work well in this setting. We propose a novel two-stage constrained actor-critic method: At stage one, we learn individual policies to optimize each auxiliary signal. At stage two, we learn a policy to (i) optimize the main signal and (ii) stay close to policies learned at the first stage, which effectively guarantees the performance of this main policy on the auxiliaries. Through extensive offline evaluations, we demonstrate effectiveness of our method over alternatives in both optimizing the main goal as well as balancing the others. We further show the advantage of our method in live experiments of short video recommendations, where it significantly outperforms other baselines in terms of both watch time and interactions. Our approach has been fully launched in the production system to optimize user experiences on the platform.

Flow-based generative models have shown remarkable success in text-to-image generation, yet fine-tuning them with intermediate feedback remains challenging, especially for continuous-time flow matching models. Most existing approaches solely learn from outcome rewards, struggling with the credit assignment problem. Alternative methods that attempt to learn a critic via direct regression on cumulative rewards often face training instabilities and model collapse in online settings. We present AC-Flow, a robust actor-critic framework that addresses these challenges through three key innovations: (1) reward shaping that provides well-normalized learning signals to enable stable intermediate value learning and gradient control, (2) a novel dual-stability mechanism that combines advantage clipping to prevent destructive policy updates with a warm-up phase that allows the critic to mature before influencing the actor, and (3) a scalable generalized critic weighting scheme that extends traditional reward-weighted methods while preserving model diversity through Wasserstein regularization. Through extensive experiments on Stable Diffusion 3, we demonstrate that AC-Flow achieves state-of-the-art performance in text-to-image alignment tasks and generalization to unseen human preference models. Our results demonstrate that even with a computationally efficient critic model, we can robustly finetune flow models without compromising generative quality, diversity, or stability.

Advantage Actor-critic (A2C) and Proximal Policy Optimization (PPO) are popular deep reinforcement learning algorithms used for game AI in recent years. A common understanding is that A2C and PPO are separate algorithms because PPO's clipped objective appears significantly different than A2C's objective. In this paper, however, we show A2C is a special case of PPO. We present theoretical justifications and pseudocode analysis to demonstrate why. To validate our claim, we conduct an empirical experiment using Stable-baselines3, showing A2C and PPO produce the exact same models when other settings are controlled.

Actor-critic algorithms have become a cornerstone in reinforcement learning (RL), leveraging the strengths of both policy-based and value-based methods. Despite recent progress in understanding their statistical efficiency, no existing work has successfully learned an epsilon-optimal policy with a sample complexity of O(1/epsilon^2) trajectories with general function approximation when strategic exploration is necessary. We address this open problem by introducing a novel actor-critic algorithm that attains a sample-complexity of O(dH^5 log|A|/epsilon^2 + d H^4 log|F|/ epsilon^2) trajectories, and accompanying T regret when the Bellman eluder dimension d does not increase with T at more than a log T rate. Here, F is the critic function class, A is the action space, and H is the horizon in the finite horizon MDP setting. Our algorithm integrates optimism, off-policy critic estimation targeting the optimal Q-function, and rare-switching policy resets. We extend this to the setting of Hybrid RL, showing that initializing the critic with offline data yields sample efficiency gains compared to purely offline or online RL. Further, utilizing access to offline data, we provide a non-optimistic provably efficient actor-critic algorithm that only additionally requires N_{off} geq c_{off}^*dH^4/epsilon^2 in exchange for omitting optimism, where c_{off}^* is the single-policy concentrability coefficient and N_{off} is the number of offline samples. This addresses another open problem in the literature. We further provide numerical experiments to support our theoretical findings.

In our work we not explicitly hint that it is a misconception to think that humans learn fast. Learning process takes time. Babies start learning to move in the restricted liquid area called placenta. Children often are limited by underdeveloped body. Even adults are not allowed to participate in complex competitions right away. However, with robots, when learning from scratch, we often don't have the privilege of waiting for dozen millions of steps. "Swaddling" regularization is responsible for restraining an agent in rapid but unstable development penalizing action strength in a specific way not affecting actions directly. The Symphony, Transitional-policy Deterministic Actor and Critic algorithm, is a concise combination of different ideas for possibility of training humanoid robots from scratch with Sample Efficiency, Sample Proximity and Safety of Actions in mind. It is no secret that continuous increase in Gaussian noise without appropriate smoothing is harmful for motors and gearboxes. Compared to Stochastic algorithms, we set a limited parametric noise and promote a reduced strength of actions, safely increasing entropy, since the actions are kind of immersed in weaker noise. When actions require more extreme values, actions rise above the weak noise. Training becomes empirically much safer for both the environment around and the robot's mechanisms. We use Fading Replay Buffer: using a fixed formula containing the hyperbolic tangent, we adjust the batch sampling probability: the memory contains a recent memory and a long-term memory trail. Fading Replay Buffer allows us to use Temporal Advantage when we improve the current Critic Network prediction compared to the exponential moving average. Temporal Advantage allows us to update Actor and Critic in one pass, as well as combine Actor and Critic in one Object and implement their Losses in one line.

Reinforcement learning has emerged as a paradigm for post-training large language models, boosting their reasoning capabilities. Such approaches compute an advantage value for each sample, reflecting better or worse performance than expected, thereby yielding both positive and negative signals for training. However, the indiscriminate mixing of the two signals in existing methods, especially from the early stages, may lead to ambiguous guidance and limited gains. To address this issue, we propose **CAPO** (**C**urriculum **A**dvantage **P**olicy **O**ptimization), an adaptive curriculum mechanism based on advantage signals. The proposed mechanism bootstraps imitation learning with positive-only advantage samples to establish robust foundations, and subsequently introduces negative signals to cultivate discriminative capabilities, thereby improving generalization across complex scenarios. Compatible with diverse optimization methods including GRPO, PPO, RLOO, and Reinforce++, our method consistently achieves stable and significant improvements in mathematical reasoning tasks, and further generalizes effectively to multimodal Graphical User Interface (GUI) reasoning scenarios, establishing itself as a versatile and robust optimization framework.

For continuous action spaces, actor-critic methods are widely used in online reinforcement learning (RL). However, unlike RL algorithms for discrete actions, which generally model the optimal value function using the Bellman optimality operator, RL algorithms for continuous actions typically model Q-values for the current policy using the Bellman operator. These algorithms for continuous actions rely exclusively on policy updates for improvement, which often results in low sample efficiency. This study examines the effectiveness of incorporating the Bellman optimality operator into actor-critic frameworks. Experiments in a simple environment show that modeling optimal values accelerates learning but leads to overestimation bias. To address this, we propose an annealing approach that gradually transitions from the Bellman optimality operator to the Bellman operator, thereby accelerating learning while mitigating bias. Our method, combined with TD3 and SAC, significantly outperforms existing approaches across various locomotion and manipulation tasks, demonstrating improved performance and robustness to hyperparameters related to optimality. The code for this study is available at https://github.com/motokiomura/annealed-q-learning.

Grounding the reasoning ability of large language models (LLMs) for embodied tasks is challenging due to the complexity of the physical world. Especially, LLM planning for multi-agent collaboration requires communication of agents or credit assignment as the feedback to re-adjust the proposed plans and achieve effective coordination. However, existing methods that overly rely on physical verification or self-reflection suffer from excessive and inefficient querying of LLMs. In this paper, we propose a novel framework for multi-agent collaboration that introduces Reinforced Advantage feedback (ReAd) for efficient self-refinement of plans. Specifically, we perform critic regression to learn a sequential advantage function from LLM-planned data, and then treat the LLM planner as an optimizer to generate actions that maximize the advantage function. It endows the LLM with the foresight to discern whether the action contributes to accomplishing the final task. We provide theoretical analysis by extending advantage-weighted regression in reinforcement learning to multi-agent systems. Experiments on Overcooked-AI and a difficult variant of RoCoBench show that ReAd surpasses baselines in success rate, and also significantly decreases the interaction steps of agents and query rounds of LLMs, demonstrating its high efficiency for grounding LLMs. More results are given at https://read-llm.github.io/.

We explore deep reinforcement learning methods for multi-agent domains. We begin by analyzing the difficulty of traditional algorithms in the multi-agent case: Q-learning is challenged by an inherent non-stationarity of the environment, while policy gradient suffers from a variance that increases as the number of agents grows. We then present an adaptation of actor-critic methods that considers action policies of other agents and is able to successfully learn policies that require complex multi-agent coordination. Additionally, we introduce a training regimen utilizing an ensemble of policies for each agent that leads to more robust multi-agent policies. We show the strength of our approach compared to existing methods in cooperative as well as competitive scenarios, where agent populations are able to discover various physical and informational coordination strategies.

We propose a reinforcement learning (RL) framework under a broad class of risk objectives, characterized by convex scoring functions. This class covers many common risk measures, such as variance, Expected Shortfall, entropic Value-at-Risk, and mean-risk utility. To resolve the time-inconsistency issue, we consider an augmented state space and an auxiliary variable and recast the problem as a two-state optimization problem. We propose a customized Actor-Critic algorithm and establish some theoretical approximation guarantees. A key theoretical contribution is that our results do not require the Markov decision process to be continuous. Additionally, we propose an auxiliary variable sampling method inspired by the alternating minimization algorithm, which is convergent under certain conditions. We validate our approach in simulation experiments with a financial application in statistical arbitrage trading, demonstrating the effectiveness of the algorithm.

Learning from off-policy data is essential for sample-efficient reinforcement learning. In the present work, we build on the insight that the advantage function can be understood as the causal effect of an action on the return, and show that this allows us to decompose the return of a trajectory into parts caused by the agent's actions (skill) and parts outside of the agent's control (luck). Furthermore, this decomposition enables us to naturally extend Direct Advantage Estimation (DAE) to off-policy settings (Off-policy DAE). The resulting method can learn from off-policy trajectories without relying on importance sampling techniques or truncating off-policy actions. We draw connections between Off-policy DAE and previous methods to demonstrate how it can speed up learning and when the proposed off-policy corrections are important. Finally, we use the MinAtar environments to illustrate how ignoring off-policy corrections can lead to suboptimal policy optimization performance.

Recent advances in reinforcement learning for foundation models, such as Group Relative Policy Optimization (GRPO), have significantly improved the performance of foundation models on reasoning tasks. Notably, the advantage function serves as a central mechanism in GRPO for ranking the trajectory importance. However, existing explorations encounter both advantage reversion and advantage mirror problems, which hinder the reasonable advantage allocation across different query samples. In this work, we propose an easy but effective GRPO strategy, Mixed Advantage Policy Optimization (MAPO). We reveal that the trajectory appears with different certainty and propose the advantage percent deviation for samples with high-certainty trajectories. Furthermore, we dynamically reweight the advantage function for samples with varying trajectory certainty, thereby adaptively configuring the advantage function to account for sample-specific characteristics. Comparison with related state-of-the-art methods, along with ablation studies on different advantage variants, validates the effectiveness of our approach.

Reinforcement learning has become a cornerstone technique for developing reasoning models in complex tasks, ranging from mathematical problem-solving to imaginary reasoning. The optimization of these models typically relies on policy gradient methods, whose efficacy hinges on the accurate estimation of an advantage function. However, prevailing methods typically employ static advantage estimation, a practice that leads to inefficient credit assignment by neglecting the dynamic utility of training samples over time. This limitation results in suboptimal policy updates, which in turn manifest as slower convergence rates and increased learning instability, as models fail to adapt to evolving sample utilities effectively. To address this problem, we introduce ADORA (Advantage Dynamics via Online Rollout Adaptation), a novel framework for policy optimization. ADORA dynamically adjusts the advantage function's weighting by adaptively categorizing training data into temporarily advantageous and disadvantageous samples, based on their evolving utility during online model rollouts. This tailored data differentiation strategy allows ADORA to be seamlessly integrated into existing policy optimization algorithms without significant architectural modifications, enabling the policy to prioritize learning from more informative experiences and thereby achieve more efficient policy updates. Extensive evaluations across diverse model families and varying data scales demonstrate that ADORA is a robust and efficient framework. It significantly enhances long reasoning in both geometric and mathematical tasks, consistently achieving notable performance gains without requiring sensitive hyperparameter tuning.

Reinforcement learning (RL) has emerged as an effective approach for enhancing the reasoning capabilities of large language models (LLMs), especially in scenarios where supervised fine-tuning (SFT) falls short due to limited chain-of-thought (CoT) data. Among RL-based post-training methods, group relative advantage estimation, as exemplified by Group Relative Policy Optimization (GRPO), has attracted considerable attention for eliminating the dependency on the value model, thereby simplifying training compared to traditional approaches like Proximal Policy Optimization (PPO). However, we observe that exsiting group relative advantage estimation method still suffers from training inefficiencies, particularly when the estimated advantage approaches zero. To address this limitation, we propose Advantage-Augmented Policy Optimization (AAPO), a novel RL algorithm that optimizes the cross-entropy (CE) loss using advantages enhanced through a momentum-based estimation scheme. This approach effectively mitigates the inefficiencies associated with group relative advantage estimation. Experimental results on multiple mathematical reasoning benchmarks demonstrate the superior performance of AAPO.

This paper investigates the problem of interactively learning behaviors communicated by a human teacher using positive and negative feedback. Much previous work on this problem has made the assumption that people provide feedback for decisions that is dependent on the behavior they are teaching and is independent from the learner's current policy. We present empirical results that show this assumption to be false -- whether human trainers give a positive or negative feedback for a decision is influenced by the learner's current policy. Based on this insight, we introduce {\em Convergent Actor-Critic by Humans} (COACH), an algorithm for learning from policy-dependent feedback that converges to a local optimum. Finally, we demonstrate that COACH can successfully learn multiple behaviors on a physical robot.

Off-policy actor-critic methods in reinforcement learning train a critic with temporal-difference updates and use it as a learning signal for the policy (actor). This design typically achieves higher sample efficiency than purely on-policy methods. However, critic networks tend to overestimate value estimates systematically. This is often addressed by introducing a pessimistic bias based on uncertainty estimates. Current methods employ ensembling to quantify the critic's epistemic uncertainty-uncertainty due to limited data and model ambiguity-to scale pessimistic updates. In this work, we propose a new algorithm called Stochastic Actor-Critic (STAC) that incorporates temporal (one-step) aleatoric uncertainty-uncertainty arising from stochastic transitions, rewards, and policy-induced variability in Bellman targets-to scale pessimistic bias in temporal-difference updates, rather than relying on epistemic uncertainty. STAC uses a single distributional critic network to model the temporal return uncertainty, and applies dropout to both the critic and actor networks for regularization. Our results show that pessimism based on a distributional critic alone suffices to mitigate overestimation, and naturally leads to risk-averse behavior in stochastic environments. Introducing dropout further improves training stability and performance by means of regularization. With this design, STAC achieves improved computational efficiency using a single distributional critic network.

Many existing reinforcement learning (RL) methods employ stochastic gradient iteration on the back end, whose stability hinges upon a hypothesis that the data-generating process mixes exponentially fast with a rate parameter that appears in the step-size selection. Unfortunately, this assumption is violated for large state spaces or settings with sparse rewards, and the mixing time is unknown, making the step size inoperable. In this work, we propose an RL methodology attuned to the mixing time by employing a multi-level Monte Carlo estimator for the critic, the actor, and the average reward embedded within an actor-critic (AC) algorithm. This method, which we call Multi-level Actor-Critic (MAC), is developed especially for infinite-horizon average-reward settings and neither relies on oracle knowledge of the mixing time in its parameter selection nor assumes its exponential decay; it, therefore, is readily applicable to applications with slower mixing times. Nonetheless, it achieves a convergence rate comparable to the state-of-the-art AC algorithms. We experimentally show that these alleviated restrictions on the technical conditions required for stability translate to superior performance in practice for RL problems with sparse rewards.

Enhancing the reasoning capabilities of large language models effectively using reinforcement learning (RL) remains a crucial challenge. Existing approaches primarily adopt two contrasting advantage estimation granularities: Token-level methods (e.g., PPO) aim to provide the fine-grained advantage signals but suffer from inaccurate estimation due to difficulties in training an accurate critic model. On the other extreme, trajectory-level methods (e.g., GRPO) solely rely on a coarse-grained advantage signal from the final reward, leading to imprecise credit assignment. To address these limitations, we propose Segment Policy Optimization (SPO), a novel RL framework that leverages segment-level advantage estimation at an intermediate granularity, achieving a better balance by offering more precise credit assignment than trajectory-level methods and requiring fewer estimation points than token-level methods, enabling accurate advantage estimation based on Monte Carlo (MC) without a critic model. SPO features three components with novel strategies: (1) flexible segment partition; (2) accurate segment advantage estimation; and (3) policy optimization using segment advantages, including a novel probability-mask strategy. We further instantiate SPO for two specific scenarios: (1) SPO-chain for short chain-of-thought (CoT), featuring novel cutpoint-based partition and chain-based advantage estimation, achieving 6-12 percentage point improvements in accuracy over PPO and GRPO on GSM8K. (2) SPO-tree for long CoT, featuring novel tree-based advantage estimation, which significantly reduces the cost of MC estimation, achieving 7-11 percentage point improvements over GRPO on MATH500 under 2K and 4K context evaluation. We make our code publicly available at https://github.com/AIFrameResearch/SPO.

Command line interface (CLI) agents are emerging as a practical paradigm for agent-computer interaction over evolving filesystems, executable command line programs, and online execution feedback. Recent work has used reinforcement learning (RL) to learn these interaction abilities from verifiable task feedback, yet few methods exploit the native structured attributes of CLI actions as learning signals. Beyond this underused action structure, CLI learning also couples two bottlenecks for coding agents. First, the agent must identify task-relevant evidence in a large codebase from partial observations. Second, sparse terminal rewards must be assigned to the actions that shape a long multi-turn trajectory. We study these bottlenecks through shell-driven information extraction and file editing tasks. For selective observation, we introduce σ-Reveal, an inference-time mechanism that selects token-budgeted context for the same CLI. For credit assignment, we propose Action Advantage Assignment (A^3), a native agentic RL method that preserves the algorithmic complexity of standard agentic RL. A^3 constructs turn-level advantages from episode-level relative feedback, abstract syntax tree (AST) based action sub-chain residuals, and tree-level trajectory margins. To further evaluate this problem setting, we construct ShellOps, a verifiable dataset suite covering CLI tasks in repository environments.

The average reward criterion is relatively less studied as most existing works in the Reinforcement Learning literature consider the discounted reward criterion. There are few recent works that present on-policy average reward actor-critic algorithms, but average reward off-policy actor-critic is relatively less explored. In this work, we present both on-policy and off-policy deterministic policy gradient theorems for the average reward performance criterion. Using these theorems, we also present an Average Reward Off-Policy Deep Deterministic Policy Gradient (ARO-DDPG) Algorithm. We first show asymptotic convergence analysis using the ODE-based method. Subsequently, we provide a finite time analysis of the resulting stochastic approximation scheme with linear function approximator and obtain an epsilon-optimal stationary policy with a sample complexity of Omega(epsilon^{-2.5}). We compare the average reward performance of our proposed ARO-DDPG algorithm and observe better empirical performance compared to state-of-the-art on-policy average reward actor-critic algorithms over MuJoCo-based environments.

We propose a novel independent and payoff-based learning framework for stochastic games that is model-free, game-agnostic, and gradient-free. The learning dynamics follow a best-response-type actor-critic architecture, where agents update their strategies (actors) using feedback from two distinct critics: a fast critic that intuitively responds to observed payoffs under limited information, and a slow critic that deliberatively approximates the solution to the underlying dynamic programming problem. Crucially, the learning process relies on non-equilibrium adaptation through smoothed best responses to observed payoffs. We establish convergence to (approximate) equilibria in two-agent zero-sum and multi-agent identical-interest stochastic games over an infinite horizon. This provides one of the first payoff-based and fully decentralized learning algorithms with theoretical guarantees in both settings. Empirical results further validate the robustness and effectiveness of the proposed approach across both classes of games.

In offline reinforcement learning, the challenge of out-of-distribution (OOD) is pronounced. To address this, existing methods often constrain the learned policy through policy regularization. However, these methods often suffer from the issue of unnecessary conservativeness, hampering policy improvement. This occurs due to the indiscriminate use of all actions from the behavior policy that generates the offline dataset as constraints. The problem becomes particularly noticeable when the quality of the dataset is suboptimal. Thus, we propose Adaptive Advantage-guided Policy Regularization (A2PR), obtaining high-advantage actions from an augmented behavior policy combined with VAE to guide the learned policy. A2PR can select high-advantage actions that differ from those present in the dataset, while still effectively maintaining conservatism from OOD actions. This is achieved by harnessing the VAE capacity to generate samples matching the distribution of the data points. We theoretically prove that the improvement of the behavior policy is guaranteed. Besides, it effectively mitigates value overestimation with a bounded performance gap. Empirically, we conduct a series of experiments on the D4RL benchmark, where A2PR demonstrates state-of-the-art performance. Furthermore, experimental results on additional suboptimal mixed datasets reveal that A2PR exhibits superior performance. Code is available at https://github.com/ltlhuuu/A2PR.

Large language models (LLMs) have demonstrated a remarkable ability to serve as general-purpose tools for various language-based tasks. Recent works have demonstrated that the efficacy of such models can be improved through iterative dialog between multiple models. While these paradigms show promise in improving model efficacy, most works in this area treat collaboration as an emergent behavior, rather than a learned behavior. In doing so, current multi-agent frameworks rely on collaborative behaviors to have been sufficiently trained into off-the-shelf models. To address this limitation, we propose ACC-Collab, an Actor-Critic based learning framework to produce a two-agent team (an actor-agent and a critic-agent) specialized in collaboration. We demonstrate that ACC-Collab outperforms SotA multi-agent techniques on a wide array of benchmarks.

Critic-free reinforcement learning methods, particularly group policies, have attracted considerable attention for their efficiency in complex tasks. However, these methods rely heavily on multiple sampling and comparisons within the policy to estimate advantage, which may cause the policy to fall into local optimum and increase computational cost. To address these issues, we propose PVPO, an efficient reinforcement learning method enhanced by an advantage reference anchor and data pre-sampling. Specifically, we use the reference model to rollout in advance and employ the calculated reward score as a reference anchor. Our approach effectively corrects the cumulative bias introduced by intra-group comparisons and significantly reduces reliance on the number of rollouts during training. Meanwhile, the reference model can assess sample difficulty during data pre-sampling, enabling effective selection of high-gain data to improve training efficiency. Moreover, PVPO is orthogonal to other advanced critic-free RL algorithms, making it compatible with and complementary to these methods. Experiments conducted on nine datasets across two domains demonstrate that PVPO achieves State-Of-The-Art (SOTA) performance. Our approach not only demonstrates robust generalization across multiple tasks, but also exhibits scalable performance across models of varying scales.

In value-based reinforcement learning methods such as deep Q-learning, function approximation errors are known to lead to overestimated value estimates and suboptimal policies. We show that this problem persists in an actor-critic setting and propose novel mechanisms to minimize its effects on both the actor and the critic. Our algorithm builds on Double Q-learning, by taking the minimum value between a pair of critics to limit overestimation. We draw the connection between target networks and overestimation bias, and suggest delaying policy updates to reduce per-update error and further improve performance. We evaluate our method on the suite of OpenAI gym tasks, outperforming the state of the art in every environment tested.

Recent work has explored optimizing LLM collaboration through Multi-Agent Reinforcement Learning (MARL). However, most MARL fine-tuning approaches rely on predefined execution protocols, which often require centralized execution. Decentralized LLM collaboration is more appealing in practice, as agents can run inference in parallel with flexible deployments. Also, current approaches use Monte Carlo methods for fine-tuning, which suffer from high variance and thus require more samples to train effectively. Actor-critic methods are prevalent in MARL for dealing with these issues, so we developed Multi-Agent Actor-Critic (MAAC) methods to optimize decentralized LLM collaboration. In this paper, we analyze when and why these MAAC methods are beneficial. We propose 2 MAAC approaches, CoLLM-CC with a Centralized Critic and CoLLM-DC with Decentralized Critics. Our experiments across writing, coding, and game-playing domains show that Monte Carlo methods and CoLLM-DC can achieve performance comparable to CoLLM-CC in short-horizon and dense-reward settings. However, they both underperform CoLLM-CC on long-horizon or sparse-reward tasks, where Monte Carlo methods require substantially more samples and CoLLM-DC struggles to converge. Our code is available at https://github.com/OpenMLRL/CoMLRL/releases/tag/v1.3.2.

A control technique is developed via Reinforcement Learning that allows arbitrary controlling of the position of an acoustic cavitation bubble in a dual-frequency standing acoustic wave field. The agent must choose the optimal pressure amplitude values to manipulate the bubble position in the range of x/lambda_0in[0.05, 0.25]. To train the agent an actor-critic off-policy algorithm (Deep Deterministic Policy Gradient) was used that supports continuous action space, which allows setting the pressure amplitude values continuously within 0 and 1, bar. A shaped reward function is formulated that minimizes the distance between the bubble and the target position and implicitly encourages the agent to perform the position control within the shortest amount of time. In some cases, the optimal control can be 7 times faster than the solution expected from the linear theory.

Policy gradient methods are reinforcement learning algorithms that adapt a parameterized policy by following a performance gradient estimate. Conventional policy gradient methods use Monte-Carlo techniques to estimate the gradient, which tend to have high variance, requiring many samples and resulting in slow convergence. We first propose a Bayesian framework for policy gradient, based on modeling the policy gradient as a Gaussian process. This reduces the number of samples needed to obtain accurate gradient estimates. Moreover, estimates of the natural gradient and a measure of the uncertainty in the gradient estimates, namely, the gradient covariance, are provided at little extra cost. Since the proposed framework considers system trajectories as its basic observable unit, it does not require the dynamics within trajectories to be of any particular form, and can be extended to partially observable problems. On the downside, it cannot exploit the Markov property when the system is Markovian. To address this, we supplement our Bayesian policy gradient framework with a new actor-critic learning model in which a Bayesian class of non-parametric critics, based on Gaussian process temporal difference learning, is used. Such critics model the action-value function as a Gaussian process, allowing Bayes rule to be used to compute the posterior distribution over action-value functions, conditioned on the observed data. Appropriate choices of the policy parameterization and of the prior covariance (kernel) between action-values yield closed-form expressions for the posterior of the gradient of the expected return with respect to the policy parameters. We perform detailed experimental comparisons of the proposed Bayesian policy gradient and actor-critic algorithms with classic Monte-Carlo based policy gradient methods, on a number of reinforcement learning problems.

Model-free deep reinforcement learning (RL) algorithms have been demonstrated on a range of challenging decision making and control tasks. However, these methods typically suffer from two major challenges: very high sample complexity and brittle convergence properties, which necessitate meticulous hyperparameter tuning. Both of these challenges severely limit the applicability of such methods to complex, real-world domains. In this paper, we propose soft actor-critic, an off-policy actor-critic deep RL algorithm based on the maximum entropy reinforcement learning framework. In this framework, the actor aims to maximize expected reward while also maximizing entropy. That is, to succeed at the task while acting as randomly as possible. Prior deep RL methods based on this framework have been formulated as Q-learning methods. By combining off-policy updates with a stable stochastic actor-critic formulation, our method achieves state-of-the-art performance on a range of continuous control benchmark tasks, outperforming prior on-policy and off-policy methods. Furthermore, we demonstrate that, in contrast to other off-policy algorithms, our approach is very stable, achieving very similar performance across different random seeds.

We propose a conceptually simple and lightweight framework for deep reinforcement learning that uses asynchronous gradient descent for optimization of deep neural network controllers. We present asynchronous variants of four standard reinforcement learning algorithms and show that parallel actor-learners have a stabilizing effect on training allowing all four methods to successfully train neural network controllers. The best performing method, an asynchronous variant of actor-critic, surpasses the current state-of-the-art on the Atari domain while training for half the time on a single multi-core CPU instead of a GPU. Furthermore, we show that asynchronous actor-critic succeeds on a wide variety of continuous motor control problems as well as on a new task of navigating random 3D mazes using a visual input.

To improve the sample efficiency of policy-gradient based reinforcement learning algorithms, we propose implicit distributional actor-critic (IDAC) that consists of a distributional critic, built on two deep generator networks (DGNs), and a semi-implicit actor (SIA), powered by a flexible policy distribution. We adopt a distributional perspective on the discounted cumulative return and model it with a state-action-dependent implicit distribution, which is approximated by the DGNs that take state-action pairs and random noises as their input. Moreover, we use the SIA to provide a semi-implicit policy distribution, which mixes the policy parameters with a reparameterizable distribution that is not constrained by an analytic density function. In this way, the policy's marginal distribution is implicit, providing the potential to model complex properties such as covariance structure and skewness, but its parameter and entropy can still be estimated. We incorporate these features with an off-policy algorithm framework to solve problems with continuous action space and compare IDAC with state-of-the-art algorithms on representative OpenAI Gym environments. We observe that IDAC outperforms these baselines in most tasks. Python code is provided.

Reinforcement learning from human feedback (RLHF) has emerged as a reliable approach to aligning large language models (LLMs) to human preferences. Among the plethora of RLHF techniques, proximal policy optimization (PPO) is of the most widely used methods. Despite its popularity, however, PPO may suffer from mode collapse, instability, and poor sample efficiency. We show that these issues can be alleviated by a novel algorithm that we refer to as Advantage-Induced Policy Alignment (APA), which leverages a squared error loss function based on the estimated advantages. We demonstrate empirically that APA consistently outperforms PPO in language tasks by a large margin, when a separate reward model is employed as the evaluator. In addition, compared with PPO, APA offers a more stable form of control over the deviation from the model's initial policy, ensuring that the model improves its performance without collapsing to deterministic output. In addition to empirical results, we also provide a theoretical justification supporting the design of our loss function.

Soft Actor Critic (SAC) algorithms show remarkable performance in complex simulated environments. A key element of SAC networks is entropy regularization, which prevents the SAC actor from optimizing against fine grained features, oftentimes transient, of the state-action value function. This results in better sample efficiency during early training. We take this idea one step further by artificially bandlimiting the target critic spatial resolution through the addition of a convolutional filter. We derive the closed form solution in the linear case and show that bandlimiting reduces the interdependency between the low and high frequency components of the state-action value approximation, allowing the critic to learn faster. In experiments, the bandlimited SAC outperformed the classic twin-critic SAC in a number of Gym environments, and displayed more stability in returns. We derive novel insights about SAC by adding a stochastic noise disturbance, a technique that is increasingly being used to learn robust policies that transfer well to the real world counterparts.

Training critiquing language models to assess and provide feedback on model outputs is a promising way to improve LLMs for complex reasoning tasks. However, existing approaches typically rely on stronger supervisors for annotating critique data. To address this, we propose Critique-RL, an online RL approach for developing critiquing language models without stronger supervision. Our approach operates on a two-player paradigm: the actor generates a response, the critic provides feedback, and the actor refines the response accordingly. We first reveal that relying solely on indirect reward signals from the actor's outputs for RL optimization often leads to unsatisfactory critics: while their helpfulness (i.e., providing constructive feedback) improves, the discriminability (i.e., determining whether a response is high-quality or not) remains poor, resulting in marginal performance gains. To overcome this, Critique-RL adopts a two-stage optimization strategy. In stage I, it reinforces the discriminability of the critic with direct rule-based reward signals; in stage II, it introduces indirect rewards based on actor refinement to improve the critic's helpfulness, while maintaining its discriminability via appropriate regularization. Extensive experiments across various tasks and models show that Critique-RL delivers substantial performance improvements. For example, it achieves a 9.02% gain on in-domain tasks and a 5.70% gain on out-of-domain tasks for Qwen2.5-7B, highlighting its potential.

To combine the advantages of Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), recent methods have integrated ''hints'' into post-training, which are prefix segments of complete reasoning trajectories, aiming for powerful knowledge expansion and reasoning generalization. However, existing hint-based RL methods typically ignore difficulty when scheduling hint ratios and estimating relative advantages, leading to unstable learning and excessive imitation of off-policy hints. In this work, we propose ADHint, which treats difficulty as a key factor in both hint-ratio schedule and relative-advantage estimation to achieve a better trade-off between exploration and imitation. Specifically, we propose Adaptive Hint with Sample Difficulty Prior, which evaluates each sample's difficulty under the policy model and accordingly schedules an appropriate hint ratio to guide its rollouts. We also introduce Consistency-based Gradient Modulation and Selective Masking for Hint Preservation to modulate token-level gradients within hints, preventing biased and destructive updates. Additionally, we propose Advantage Estimation with Rollout Difficulty Posterior, which leverages the relative difficulty of rollouts with and without hints to estimate their respective advantages, thereby achieving more balanced updates. Extensive experiments across diverse modalities, model scales, and domains demonstrate that ADHint delivers superior reasoning ability and out-of-distribution generalization, consistently surpassing existing methods in both pass@1 and avg@8. Our code and dataset will be made publicly available upon paper acceptance.

Discrete-action reinforcement learning algorithms often falter in tasks with high-dimensional discrete action spaces due to the vast number of possible actions. A recent advancement leverages value-decomposition, a concept from multi-agent reinforcement learning, to tackle this challenge. This study delves deep into the effects of this value-decomposition, revealing that whilst it curtails the over-estimation bias inherent to Q-learning algorithms, it amplifies target variance. To counteract this, we present an ensemble of critics to mitigate target variance. Moreover, we introduce a regularisation loss that helps to mitigate the effects that exploratory actions in one dimension can have on the value of optimal actions in other dimensions. Our novel algorithm, REValueD, tested on discretised versions of the DeepMind Control Suite tasks, showcases superior performance, especially in the challenging humanoid and dog tasks. We further dissect the factors influencing REValueD's performance, evaluating the significance of the regularisation loss and the scalability of REValueD with increasing sub-actions per dimension.

Long-horizon robotic manipulation remains challenging for reinforcement learning (RL) because sparse rewards provide limited guidance for credit assignment. Practical policy improvement thus relies on richer intermediate supervision, such as dense progress rewards, which are costly to obtain and ill-suited to non-monotonic behaviors such as backtracking and recovery. To address this, we propose Advantage Reward Modeling (ARM), a framework that shifts from hard-to-quantify absolute progress to estimating relative advantage. We introduce a cost-effective tri-state labeling strategy -- Progressive, Regressive, and Stagnant -- that reduces human cognitive overhead while ensuring high cross-annotator consistency. By training on these intuitive signals, ARM enables automated progress annotation for both complete demonstrations and fragmented DAgger-style data. Integrating ARM into an offline RL pipeline allows for adaptive action-reward reweighting, effectively filtering suboptimal samples. Our approach achieves a 99.4% success rate on a challenging long-horizon towel-folding task, demonstrating improved stability and data efficiency over current VLA baselines with near-zero human intervention during policy training.

Steering language generation towards objectives or away from undesired content has been a long-standing goal in utilizing language models (LM). Recent work has demonstrated reinforcement learning and weighted decoding as effective approaches to achieve a higher level of language control and quality with pros and cons. In this work, we propose a novel critic decoding method for controlled language generation (CriticControl) that combines the strengths of reinforcement learning and weighted decoding. Specifically, we adopt the actor-critic framework to train an LM-steering critic from non-differentiable reward models. And similar to weighted decoding, our method freezes the language model and manipulates the output token distribution using called critic, improving training efficiency and stability. Evaluation of our method on three controlled generation tasks, namely topic control, sentiment control, and detoxification, shows that our approach generates more coherent and well-controlled texts than previous methods. In addition, CriticControl demonstrates superior generalization ability in zero-shot settings. Human evaluation studies also corroborate our findings.

Policy gradient methods rely on a baseline to measure the relative advantage of an action, ensuring the model reinforces behaviors that outperform its current average capability. In the training of Large Language Models (LLMs) using Actor-Critic methods (e.g., PPO), this baseline is typically estimated by a Value Model (Critic) often as large as the policy model itself. However, as the policy continuously evolves, the value model requires expensive, synchronous incremental training to accurately track the shifting capabilities of the policy. To avoid this overhead, Group Relative Policy Optimization (GRPO) eliminates the coupled value model by using the average reward of a group of rollouts as the baseline; yet, this approach necessitates extensive sampling to maintain estimation stability. In this paper, we propose V_0, a Generalist Value Model capable of estimating the expected performance of any model on unseen prompts without requiring parameter updates. We reframe value estimation by treating the policy's dynamic capability as an explicit context input; specifically, we leverage a history of instruction-performance pairs to dynamically profile the model, departing from the traditional paradigm that relies on parameter fitting to perceive capability shifts. Focusing on value estimation at State Zero (i.e., the initial prompt, hence V_0), our model serves as a critical resource scheduler. During GRPO training, V_0 predicts success rates prior to rollout, allowing for efficient sampling budget allocation; during deployment, it functions as a router, dispatching instructions to the most cost-effective and suitable model. Empirical results demonstrate that V_0 significantly outperforms heuristic budget allocation and achieves a Pareto-optimal trade-off between performance and cost in LLM routing tasks.

We consider an improper reinforcement learning setting where a learner is given M base controllers for an unknown Markov decision process, and wishes to combine them optimally to produce a potentially new controller that can outperform each of the base ones. This can be useful in tuning across controllers, learnt possibly in mismatched or simulated environments, to obtain a good controller for a given target environment with relatively few trials. Towards this, we propose two algorithms: (1) a Policy Gradient-based approach; and (2) an algorithm that can switch between a simple Actor-Critic (AC) based scheme and a Natural Actor-Critic (NAC) scheme depending on the available information. Both algorithms operate over a class of improper mixtures of the given controllers. For the first case, we derive convergence rate guarantees assuming access to a gradient oracle. For the AC-based approach we provide convergence rate guarantees to a stationary point in the basic AC case and to a global optimum in the NAC case. Numerical results on (i) the standard control theoretic benchmark of stabilizing an cartpole; and (ii) a constrained queueing task show that our improper policy optimization algorithm can stabilize the system even when the base policies at its disposal are unstable.

Soft Actor-Critic is a state-of-the-art reinforcement learning algorithm for continuous action settings that is not applicable to discrete action settings. Many important settings involve discrete actions, however, and so here we derive an alternative version of the Soft Actor-Critic algorithm that is applicable to discrete action settings. We then show that, even without any hyperparameter tuning, it is competitive with the tuned model-free state-of-the-art on a selection of games from the Atari suite.

Recently, test-time scaling Large Language Models (LLMs) have demonstrated exceptional reasoning capabilities across scientific and professional tasks by generating long chains-of-thought (CoT). As a crucial component for developing these reasoning models, reinforcement learning (RL), exemplified by Proximal Policy Optimization (PPO) and its variants, allows models to learn through trial and error. However, PPO can be time-consuming due to its inherent on-policy nature, which is further exacerbated by increasing response lengths. In this work, we propose Truncated Proximal Policy Optimization (T-PPO), a novel extension to PPO that improves training efficiency by streamlining policy update and length-restricted response generation. T-PPO mitigates the issue of low hardware utilization, an inherent drawback of fully synchronized long-generation procedures, where resources often sit idle during the waiting periods for complete rollouts. Our contributions are two-folds. First, we propose Extended Generalized Advantage Estimation (EGAE) for advantage estimation derived from incomplete responses while maintaining the integrity of policy learning. Second, we devise a computationally optimized mechanism that allows for the independent optimization of the policy and value models. By selectively filtering prompt and truncated tokens, this mechanism reduces redundant computations and accelerates the training process without sacrificing convergence performance. We demonstrate the effectiveness and efficacy of T-PPO on AIME 2024 with a 32B base model. The experimental results show that T-PPO improves the training efficiency of reasoning LLMs by up to 2.5x and outperforms its existing competitors.

Offline reinforcement learning faces a significant challenge of value over-estimation due to the distributional drift between the dataset and the current learned policy, leading to learning failure in practice. The common approach is to incorporate a penalty term to reward or value estimation in the Bellman iterations. Meanwhile, to avoid extrapolation on out-of-distribution (OOD) states and actions, existing methods focus on conservative Q-function estimation. In this paper, we propose Conservative State Value Estimation (CSVE), a new approach that learns conservative V-function via directly imposing penalty on OOD states. Compared to prior work, CSVE allows more effective in-data policy optimization with conservative value guarantees. Further, we apply CSVE and develop a practical actor-critic algorithm in which the critic does the conservative value estimation by additionally sampling and penalizing the states around the dataset, and the actor applies advantage weighted updates extended with state exploration to improve the policy. We evaluate in classic continual control tasks of D4RL, showing that our method performs better than the conservative Q-function learning methods and is strongly competitive among recent SOTA methods.

The varying significance of distinct primitive behaviors during the policy learning process has been overlooked by prior model-free RL algorithms. Leveraging this insight, we explore the causal relationship between different action dimensions and rewards to evaluate the significance of various primitive behaviors during training. We introduce a causality-aware entropy term that effectively identifies and prioritizes actions with high potential impacts for efficient exploration. Furthermore, to prevent excessive focus on specific primitive behaviors, we analyze the gradient dormancy phenomenon and introduce a dormancy-guided reset mechanism to further enhance the efficacy of our method. Our proposed algorithm, ACE: Off-policy Actor-critic with Causality-aware Entropy regularization, demonstrates a substantial performance advantage across 29 diverse continuous control tasks spanning 7 domains compared to model-free RL baselines, which underscores the effectiveness, versatility, and efficient sample efficiency of our approach. Benchmark results and videos are available at https://ace-rl.github.io/.

Despite the success of Random Network Distillation (RND) in various domains, it was shown as not discriminative enough to be used as an uncertainty estimator for penalizing out-of-distribution actions in offline reinforcement learning. In this paper, we revisit these results and show that, with a naive choice of conditioning for the RND prior, it becomes infeasible for the actor to effectively minimize the anti-exploration bonus and discriminativity is not an issue. We show that this limitation can be avoided with conditioning based on Feature-wise Linear Modulation (FiLM), resulting in a simple and efficient ensemble-free algorithm based on Soft Actor-Critic. We evaluate it on the D4RL benchmark, showing that it is capable of achieving performance comparable to ensemble-based methods and outperforming ensemble-free approaches by a wide margin.

Reinforcement learning has become a powerful paradigm for post-training large language model agents, yet credit assignment in multi-turn environments remains a challenge. Agents often receive sparse, trajectory-level rewards only at the end of an episode, making it difficult to determine which intermediate actions contributed to success or failure. As a result, propagating delayed outcomes back to individual decision steps without relying on costly auxiliary value models remains an open problem. We propose Generalized Advantage Grouped Policy Optimization (GAGPO), a critic-free reinforcement learning method for precise, step-aligned temporal credit assignment. GAGPO constructs a non-parametric grouped value proxy from sampled rollouts and uses it to compute TD/GAE-style temporal advantages, recursively propagating outcome supervision backward through time. Combined with group-wise advantage normalization and an action-level importance ratio, GAGPO extracts stable, localized optimization signals directly from multi-turn trajectories. Experiments on ALFWorld and WebShop show that GAGPO outperforms strong reinforcement learning baselines. Further analyses demonstrate faster early-stage learning, improved interaction efficiency, and smoother optimization dynamics, suggesting that GAGPO offers a simple yet effective framework for multi-turn agentic reinforcement learning.

Developing an agent capable of adapting to unseen environments remains a difficult challenge in imitation learning. This work presents Adaptive Return-conditioned Policy (ARP), an efficient framework designed to enhance the agent's generalization ability using natural language task descriptions and pre-trained multimodal encoders. Our key idea is to calculate a similarity between visual observations and natural language instructions in the pre-trained multimodal embedding space (such as CLIP) and use it as a reward signal. We then train a return-conditioned policy using expert demonstrations labeled with multimodal rewards. Because the multimodal rewards provide adaptive signals at each timestep, our ARP effectively mitigates the goal misgeneralization. This results in superior generalization performances even when faced with unseen text instructions, compared to existing text-conditioned policies. To improve the quality of rewards, we also introduce a fine-tuning method for pre-trained multimodal encoders, further enhancing the performance. Video demonstrations and source code are available on the project website: https://sites.google.com/view/2023arp.

This paper investigates the application of Deep Reinforcement Learning (DRL) for Environment, Social, and Governance (ESG) financial portfolio management, with a specific focus on the potential benefits of ESG score-based market regulation. We leveraged an Advantage Actor-Critic (A2C) agent and conducted our experiments using environments encoded within the OpenAI Gym, adapted from the FinRL platform. The study includes a comparative analysis of DRL agent performance under standard Dow Jones Industrial Average (DJIA) market conditions and a scenario where returns are regulated in line with company ESG scores. In the ESG-regulated market, grants were proportionally allotted to portfolios based on their returns and ESG scores, while taxes were assigned to portfolios below the mean ESG score of the index. The results intriguingly reveal that the DRL agent within the ESG-regulated market outperforms the standard DJIA market setup. Furthermore, we considered the inclusion of ESG variables in the agent state space, and compared this with scenarios where such data were excluded. This comparison adds to the understanding of the role of ESG factors in portfolio management decision-making. We also analyze the behaviour of the DRL agent in IBEX 35 and NASDAQ-100 indexes. Both the A2C and Proximal Policy Optimization (PPO) algorithms were applied to these additional markets, providing a broader perspective on the generalization of our findings. This work contributes to the evolving field of ESG investing, suggesting that market regulation based on ESG scoring can potentially improve DRL-based portfolio management, with significant implications for sustainable investing strategies.

We show that offline actor-critic reinforcement learning can scale to large models - such as transformers - and follows similar scaling laws as supervised learning. We find that offline actor-critic algorithms can outperform strong, supervised, behavioral cloning baselines for multi-task training on a large dataset containing both sub-optimal and expert behavior on 132 continuous control tasks. We introduce a Perceiver-based actor-critic model and elucidate the key model features needed to make offline RL work with self- and cross-attention modules. Overall, we find that: i) simple offline actor critic algorithms are a natural choice for gradually moving away from the currently predominant paradigm of behavioral cloning, and ii) via offline RL it is possible to learn multi-task policies that master many domains simultaneously, including real robotics tasks, from sub-optimal demonstrations or self-generated data.

Model-free deep reinforcement learning (RL) algorithms have been successfully applied to a range of challenging sequential decision making and control tasks. However, these methods typically suffer from two major challenges: high sample complexity and brittleness to hyperparameters. Both of these challenges limit the applicability of such methods to real-world domains. In this paper, we describe Soft Actor-Critic (SAC), our recently introduced off-policy actor-critic algorithm based on the maximum entropy RL framework. In this framework, the actor aims to simultaneously maximize expected return and entropy. That is, to succeed at the task while acting as randomly as possible. We extend SAC to incorporate a number of modifications that accelerate training and improve stability with respect to the hyperparameters, including a constrained formulation that automatically tunes the temperature hyperparameter. We systematically evaluate SAC on a range of benchmark tasks, as well as real-world challenging tasks such as locomotion for a quadrupedal robot and robotic manipulation with a dexterous hand. With these improvements, SAC achieves state-of-the-art performance, outperforming prior on-policy and off-policy methods in sample-efficiency and asymptotic performance. Furthermore, we demonstrate that, in contrast to other off-policy algorithms, our approach is very stable, achieving similar performance across different random seeds. These results suggest that SAC is a promising candidate for learning in real-world robotics tasks.

Existing imitation learning methods mainly focus on making an agent effectively mimic a demonstrated behavior, but do not address the potential contradiction between the behavior style and the objective of a task. There is a general lack of efficient methods that allow an agent to partially imitate a demonstrated behavior to varying degrees, while completing the main objective of a task. In this paper we propose a method called Regularized Soft Actor-Critic which formulates the main task and the imitation task under the Constrained Markov Decision Process framework (CMDP). The main task is defined as the maximum entropy objective used in Soft Actor-Critic (SAC) and the imitation task is defined as a constraint. We evaluate our method on continuous control tasks relevant to video games applications.

The vast majority of Reinforcement Learning methods is largely impacted by the computation effort and data requirements needed to obtain effective estimates of action-value functions, which in turn determine the quality of the overall performance and the sample-efficiency of the learning procedure. Typically, action-value functions are estimated through an iterative scheme that alternates the application of an empirical approximation of the Bellman operator and a subsequent projection step onto a considered function space. It has been observed that this scheme can be potentially generalized to carry out multiple iterations of the Bellman operator at once, benefiting the underlying learning algorithm. However, till now, it has been challenging to effectively implement this idea, especially in high-dimensional problems. In this paper, we introduce iterated Q-Network (i-QN), a novel principled approach that enables multiple consecutive Bellman updates by learning a tailored sequence of action-value functions where each serves as the target for the next. We show that i-QN is theoretically grounded and that it can be seamlessly used in value-based and actor-critic methods. We empirically demonstrate the advantages of i-QN in Atari 2600 games and MuJoCo continuous control problems.

Large reasoning models (LRMs) aim to solve diverse and complex problems through structured reasoning. Recent advances in group-based policy optimization methods have shown promise in enabling stable advantage estimation without reliance on process-level annotations. However, these methods rely on advantage gaps induced by high-quality samples within the same batch, which makes the training process fragile and inefficient when intra-group advantages collapse under challenging tasks. To address these problems, we propose a reinforcement learning mechanism named \textbf{R^3} that along three directions: (1) a cross-context \underline{\textbf{R}eplay} strategy that maintains the intra-group advantage by recalling valuable examples from historical trajectories of the same query, (2) an in-context self-\underline{\textbf{R}eflection} mechanism enabling models to refine outputs by leveraging past failures, and (3) a structural entropy \underline{\textbf{R}anking reward}, which assigns relative rewards to truncated or failed samples by ranking responses based on token-level entropy patterns, capturing both local exploration and global stability. We implement our method on Deepseek-R1-Distill-Qwen-1.5B and train it on the DeepscaleR-40k in the math domain. Experiments demonstrate our method achieves SoTA performance on several math benchmarks, representing significant improvements and fewer reasoning tokens over the base models. Code and model will be released.

Reinforcement Learning from Verifier Rewards (RLVR) has emerged as a widely used approach for post-training large language models on reasoning tasks, with group-based methods such as GRPO and its variants gaining broad adoption. These methods rely on group-relative advantage estimation to avoid learned critics, yet its theoretical properties remain poorly understood. In this work, we uncover a fundamental issue of group-based RL: the group-relative advantage estimator is inherently biased relative to the true (expected) advantage. We provide the first theoretical analysis showing that it systematically underestimates advantages for hard prompts and overestimates them for easy prompts, leading to imbalanced exploration and exploitation. To address this issue, we propose History-Aware Adaptive Difficulty Weighting (HA-DW), an adaptive reweighting scheme that adjusts advantage estimates based on an evolving difficulty anchor and training dynamics. Both theoretical analysis and experiments on five mathematical reasoning benchmarks demonstrate that HA-DW consistently improves performance when integrated into GRPO and its variants. Our results suggest that correcting biased advantage estimation is critical for robust and efficient RLVR training.

Reinforcement learning (RL)-based fine-tuning has emerged as a powerful approach for aligning diffusion models with black-box objectives. Proximal policy optimization (PPO) is the most popular choice of method for policy optimization. While effective in terms of performance, PPO is highly sensitive to hyper-parameters and involves substantial computational overhead. REINFORCE, on the other hand, mitigates some computational complexities such as high memory overhead and sensitive hyper-parameter tuning, but has suboptimal performance due to high-variance and sample inefficiency. While the variance of the REINFORCE can be reduced by sampling multiple actions per input prompt and using a baseline correction term, it still suffers from sample inefficiency. To address these challenges, we systematically analyze the efficiency-effectiveness trade-off between REINFORCE and PPO, and propose leave-one-out PPO (LOOP), a novel RL for diffusion fine-tuning method. LOOP combines variance reduction techniques from REINFORCE, such as sampling multiple actions per input prompt and a baseline correction term, with the robustness and sample efficiency of PPO via clipping and importance sampling. Our results demonstrate that LOOP effectively improves diffusion models on various black-box objectives, and achieves a better balance between computational efficiency and performance.

We present Self-Play Preference Optimization (SPO), an algorithm for reinforcement learning from human feedback. Our approach is minimalist in that it does not require training a reward model nor unstable adversarial training and is therefore rather simple to implement. Our approach is maximalist in that it provably handles non-Markovian, intransitive, and stochastic preferences while being robust to the compounding errors that plague offline approaches to sequential prediction. To achieve the preceding qualities, we build upon the concept of a Minimax Winner (MW), a notion of preference aggregation from the social choice theory literature that frames learning from preferences as a zero-sum game between two policies. By leveraging the symmetry of this game, we prove that rather than using the traditional technique of dueling two policies to compute the MW, we can simply have a single agent play against itself while maintaining strong convergence guarantees. Practically, this corresponds to sampling multiple trajectories from a policy, asking a rater or preference model to compare them, and then using the proportion of wins as the reward for a particular trajectory. We demonstrate that on a suite of continuous control tasks, we are able to learn significantly more efficiently than reward-model based approaches while maintaining robustness to the intransitive and stochastic preferences that frequently occur in practice when aggregating human judgments.

In this work, we investigate how explicitly modeling problem's difficulty prior information shapes the effectiveness of reinforcement learning based fine-tuning for multimodal reasoning. Our exploration mainly comprises of following three perspective: First, through offline data curation, we analyze the U-shaped difficulty distribution of two given datasets using the base model by multi-round sampling, and then filter out prompts that are either too simple or extremely difficult to provide meaningful gradients and perform subsequent two-stage training. Second, we implement an online advantage differentiation, computing group-wise empirical accuracy as a difficulty proxy to adaptively reweight advantages estimation, providing stronger learning signals for more challenging problems. Finally, we introduce difficulty hints as explicit prompts for more complex samples in the second training stage, encouraging the model to calibrate its reasoning depth and perform reflective validation checks. Our comprehensive approach demonstrates significant performances across various multi-modal mathematical reasoning benchmarks with only 2K+0.6K two-stage training data.

Large language models (LLMs) have recently transformed from text-based assistants to autonomous agents capable of planning, reasoning, and iteratively improving their actions. While numerical reward signals and verifiers can effectively rank candidate actions, they often provide limited contextual guidance. In contrast, natural language feedback better aligns with the generative capabilities of LLMs, providing richer and more actionable suggestions. However, parsing and implementing this feedback effectively can be challenging for LLM-based agents. In this work, we introduce Critique-Guided Improvement (CGI), a novel two-player framework, comprising an actor model that explores an environment and a critic model that generates detailed nature language feedback. By training the critic to produce fine-grained assessments and actionable revisions, and the actor to utilize these critiques, our approach promotes more robust exploration of alternative strategies while avoiding local optima. Experiments in three interactive environments show that CGI outperforms existing baselines by a substantial margin. Notably, even a small critic model surpasses GPT-4 in feedback quality. The resulting actor achieves state-of-the-art performance, demonstrating the power of explicit iterative guidance to enhance decision-making in LLM-based agents.

Training LLMs as interactive agents for multi-turn decision-making remains challenging, particularly in long-horizon tasks with sparse and delayed rewards, where agents must execute extended sequences of actions before receiving meaningful feedback. Most existing reinforcement learning (RL) approaches model LLM agents as flat policies operating at a single time scale, selecting one action at each turn. In sparse-reward settings, such flat policies must propagate credit across the entire trajectory without explicit temporal abstraction, which often leads to unstable optimization and inefficient credit assignment. We propose HiPER, a novel Hierarchical Plan-Execute RL framework that explicitly separates high-level planning from low-level execution. HiPER factorizes the policy into a high-level planner that proposes subgoals and a low-level executor that carries them out over multiple action steps. To align optimization with this structure, we introduce a key technique called hierarchical advantage estimation (HAE), which carefully assigns credit at both the planning and execution levels. By aggregating returns over the execution of each subgoal and coordinating updates across the two levels, HAE provides an unbiased gradient estimator and provably reduces variance compared to flat generalized advantage estimation. Empirically, HiPER achieves state-of-the-art performance on challenging interactive benchmarks, reaching 97.4\% success on ALFWorld and 83.3\% on WebShop with Qwen2.5-7B-Instruct (+6.6\% and +8.3\% over the best prior method), with especially large gains on long-horizon tasks requiring multiple dependent subtasks. These results highlight the importance of explicit hierarchical decomposition for scalable RL training of multi-turn LLM agents.

Reinforcement Learning with Human Feedback (RLHF) has achieved great success in aligning large language models (LLMs) with human preferences. Prevalent RLHF approaches are reward-based, following the Bradley-Terry (BT) model assumption, which may not fully capture the complexity of human preferences. In this paper, we explore RLHF under a general preference framework and approach it from a game-theoretic perspective. Specifically, we formulate the problem as a two-player game and propose a novel algorithm, iterative Nash policy optimization (INPO). The key idea is to let the policy play against itself via no-regret learning, thereby approximating the Nash policy. Unlike previous methods, INPO bypasses the need for estimating the expected win rate for individual responses, which typically incurs high computational or annotation costs. Instead, we introduce a new loss objective that is directly minimized over a preference dataset. We provide theoretical analysis for our approach and demonstrate its effectiveness through experiments on various representative benchmarks. With an LLaMA-3-8B-based SFT model, INPO achieves a 41.5% length-controlled win rate on AlpacaEval 2.0 and a 38.3% win rate on Arena-Hard, showing substantial improvement over the state-of-the-art iterative algorithm [Dong et al., 2024] under the BT model assumption. Additionally, our ablation study highlights the benefits of incorporating KL regularization for response length control.

Diffusion models are powerful generative models that allow for precise control over the characteristics of the generated samples. While these diffusion models trained on large datasets have achieved success, there is often a need to introduce additional controls in downstream fine-tuning processes, treating these powerful models as pre-trained diffusion models. This work presents a novel method based on reinforcement learning (RL) to add such controls using an offline dataset comprising inputs and labels. We formulate this task as an RL problem, with the classifier learned from the offline dataset and the KL divergence against pre-trained models serving as the reward functions. Our method, CTRL (Conditioning pre-Trained diffusion models with Reinforcement Learning), produces soft-optimal policies that maximize the abovementioned reward functions. We formally demonstrate that our method enables sampling from the conditional distribution with additional controls during inference. Our RL-based approach offers several advantages over existing methods. Compared to classifier-free guidance, it improves sample efficiency and can greatly simplify dataset construction by leveraging conditional independence between the inputs and additional controls. Additionally, unlike classifier guidance, it eliminates the need to train classifiers from intermediate states to additional controls. The code is available at https://github.com/zhaoyl18/CTRL.

Current critic-free RL methods for large reasoning models suffer from severe inefficiency when training on positive homogeneous prompts (where all rollouts are correct), resulting in waste of rollouts due to zero advantage estimates. We introduce a radically simple yet powerful solution to Mine intrinsic mastery (Miner), that repurposes the policy's intrinsic uncertainty as a self-supervised reward signal, with no external supervision, auxiliary models, or additional inference cost. Our method pioneers two key innovations: (1) a token-level focal credit assignment mechanism that dynamically amplifies gradients on critical uncertain tokens while suppressing overconfident ones, and (2) adaptive advantage calibration to seamlessly integrate intrinsic and verifiable rewards. Evaluated across six reasoning benchmarks on Qwen3-4B and Qwen3-8B base models, Miner achieves state-of-the-art performance among the other four algorithms, yielding up to 4.58 absolute gains in Pass@1 and 6.66 gains in Pass@K compared to GRPO. Comparison with other methods targeted at exploration enhancement further discloses the superiority of the two newly proposed innovations. This demonstrates that latent uncertainty exploitation is both necessary and sufficient for efficient and scalable RL training of reasoning models.

Recent advances in reasoning with large language models (LLMs) have shown the effectiveness of Monte Carlo Tree Search (MCTS) for generating high-quality intermediate trajectories, particularly in math and symbolic domains. Inspired by this, we explore how MCTS-derived trajectories, traditionally used for training value or reward models, can be repurposed to improve policy optimization in preference-based reinforcement learning (RL). Specifically, we focus on Group Relative Policy Optimization (GRPO), a recent algorithm that enables preference-consistent policy learning without value networks. We propose a staged GRPO training paradigm where completions are derived from partially revealed MCTS rollouts, introducing a novel tree-structured setting for advantage estimation. This leads to a rich class of prefix-conditioned reward signals, which we analyze theoretically and empirically. Our initial results indicate that while structured advantage estimation can stabilize updates and better reflect compositional reasoning quality, challenges such as advantage saturation and reward signal collapse remain. We propose heuristic and statistical solutions to mitigate these issues and discuss open challenges for learning under staged or tree-like reward structures.

Adversarial imitation learning (AIL) has stood out as a dominant framework across various imitation learning (IL) applications, with Discriminator Actor Critic (DAC) (Kostrikov et al.,, 2019) demonstrating the effectiveness of off-policy learning algorithms in improving sample efficiency and scalability to higher-dimensional observations. Despite DAC's empirical success, the original AIL objective is on-policy and DAC's ad-hoc application of off-policy training does not guarantee successful imitation (Kostrikov et al., 2019; 2020). Follow-up work such as ValueDICE (Kostrikov et al., 2020) tackles this issue by deriving a fully off-policy AIL objective. Instead in this work, we develop a novel and principled AIL algorithm via the framework of boosting. Like boosting, our new algorithm, AILBoost, maintains an ensemble of properly weighted weak learners (i.e., policies) and trains a discriminator that witnesses the maximum discrepancy between the distributions of the ensemble and the expert policy. We maintain a weighted replay buffer to represent the state-action distribution induced by the ensemble, allowing us to train discriminators using the entire data collected so far. In the weighted replay buffer, the contribution of the data from older policies are properly discounted with the weight computed based on the boosting framework. Empirically, we evaluate our algorithm on both controller state-based and pixel-based environments from the DeepMind Control Suite. AILBoost outperforms DAC on both types of environments, demonstrating the benefit of properly weighting replay buffer data for off-policy training. On state-based environments, DAC outperforms ValueDICE and IQ-Learn (Gary et al., 2021), achieving competitive performance with as little as one expert trajectory.

Reinforcement Learning has become a standard paradigm for aligning Large Language Models with human intent and task requirements. While Group Relative Policy Optimization offers an efficient, value-model-free alternative to Proximal Policy Optimization, adapting it to real-world multi-reward settings remains challenging. Standard scalarization practices, such as Reward Combination and Advantage Combination, suffer from significant drawbacks: Reward Combination frequently generates advantages with excessively large squared magnitudes that lead to training instability, while Advantage Combination relies on static hyperparameters and ignores cross-objective correlations. To address these limitations, we propose Dynamic Variance-adaptive Advantage Optimization (DVAO), which dynamically adjusts combination weights based on the empirical reward variance of each objective within a rollout group, effectively up-weighting objectives with a stronger learning signal while suppressing noisy ones. We mathematically prove that DVAO maintains bounded advantage magnitudes for stable training and introduces a self-adaptive cross-objective regularization mechanism. Extensive experiments on mathematical reasoning and tool-use benchmarks using Qwen3 and Qwen2.5 models demonstrate that DVAO significantly outperforms baseline methods, achieving a superior multi-objective Pareto frontier and robust training stability.

In the highly volatile and uncertain global financial markets, traditional quantitative trading models relying on statistical modeling or empirical rules often fail to adapt to dynamic market changes and black swan events due to rigid assumptions and limited generalization. To address these issues, this paper proposes QTMRL (Quantitative Trading Multi-Indicator Reinforcement Learning), an intelligent trading agent combining multi-dimensional technical indicators with reinforcement learning (RL) for adaptive and stable portfolio management. We first construct a comprehensive multi-indicator dataset using 23 years of S&P 500 daily OHLCV data (2000-2022) for 16 representative stocks across 5 sectors, enriching raw data with trend, volatility, and momentum indicators to capture holistic market dynamics. Then we design a lightweight RL framework based on the Advantage Actor-Critic (A2C) algorithm, including data processing, A2C algorithm, and trading agent modules to support policy learning and actionable trading decisions. Extensive experiments compare QTMRL with 9 baselines (e.g., ARIMA, LSTM, moving average strategies) across diverse market regimes, verifying its superiority in profitability, risk adjustment, and downside risk control. The code of QTMRL is publicly available at https://github.com/ChenJiahaoJNU/QTMRL.git

Reinforcement learning (RL) is pivotal for enabling large language models (LLMs) to generate long chains of thought (CoT) for complex tasks like math and reasoning. However, Proximal Policy Optimization (PPO), effective in many RL scenarios, fails in long CoT tasks. This paper identifies that value initialization bias and reward signal decay are the root causes of PPO's failure. We propose Value-Calibrated PPO (VC-PPO) to address these issues. In VC-PPO, the value model is pretrained to tackle initialization bias, and the Generalized Advantage Estimation (GAE) computation is decoupled between the actor and critic to mitigate reward signal decay. Experiments on the American Invitational Mathematics Examination (AIME) show that VC-PPO significantly boosts PPO performance. Ablation studies show that techniques in VC-PPO are essential in enhancing PPO for long CoT tasks.

Large Language Models (LLMs) have demonstrated remarkable capabilities, enabling language agents to excel at single-turn tasks. However, their application to complex, multi-step, and long-horizon tasks remains challenging. While reinforcement learning (RL) offers a promising avenue for addressing these challenges, mainstream approaches typically rely solely on sparse, outcome-based rewards, a limitation that becomes especially problematic for group-based RL algorithms lacking critic models, such as Group Relative Policy Optimization (GRPO). In such methods, uniformly rewarding or penalizing all actions within a trajectory can lead to training instability and suboptimal policies, because beneficial and detrimental actions are often entangled across multi-step interactions. To address this challenge, we propose SALT, a novel and lightweight framework that provides a finer-grained advantage assignment, derived solely from outcome rewards. We achieve this by constructing a graph from trajectories of the same prompt, which allows us to quantify the quality of each step and assign advantages accordingly. Crucially, SALT is designed as a plug-and-play module that seamlessly integrates with existing group-based RL algorithms, requiring no modifications to the rollout procedure and introducing negligible computational overhead. Extensive experiments on the WebShop, ALFWorld, and AppWorld benchmarks with various model sizes demonstrate that SALT consistently improves performance. We also conduct a thorough analysis to validate the design choices behind SALT and offer actionable insights.

Recently, multimodal large language models (MLLMs) have demonstrated strong visual understanding and decision-making capabilities, enabling the exploration of autonomously improving MLLMs in unknown environments. However, external feedback like human or environmental feedback is not always available. To address this challenge, existing methods primarily focus on enhancing the decision-making capabilities of MLLMs through voting and scoring mechanisms, while little effort has been paid to improving the environmental comprehension of MLLMs in unknown environments. To fully unleash the self-learning potential of MLLMs, we propose a novel actor-critic self-learning paradigm, dubbed SELU, inspired by the actor-critic paradigm in reinforcement learning. The critic employs self-asking and hindsight relabeling to extract knowledge from interaction trajectories collected by the actor, thereby augmenting its environmental comprehension. Simultaneously, the actor is improved by the self-feedback provided by the critic, enhancing its decision-making. We evaluate our method in the AI2-THOR and VirtualHome environments, and SELU achieves critic improvements of approximately 28% and 30%, and actor improvements of about 20% and 24% via self-learning.

We develop policy gradients methods for stochastic control with exit time in a model-free setting. We propose two types of algorithms for learning either directly the optimal policy or by learning alternately the value function (critic) and the optimal control (actor). The use of randomized policies is crucial for overcoming notably the issue related to the exit time in the gradient computation. We demonstrate the effectiveness of our approach by implementing our numerical schemes in the application to the problem of share repurchase pricing. Our results show that the proposed policy gradient methods outperform PDE or other neural networks techniques in a model-based setting. Furthermore, our algorithms are flexible enough to incorporate realistic market conditions like e.g. price impact or transaction costs.

Recent advances in large language models (LLMs) highlight the importance of post training techniques for improving reasoning and mathematical ability. Group Relative Policy Optimization (GRPO) has shown promise in this domain by combining group relative advantage estimation, PPO style clipping, and KL regularization. However, its complexity raises the question of whether all components are necessary for fostering reasoning behaviors. We conduct a systematic analysis of GRPO and identify two key findings: (1) incorporating negative feedback is essential training solely on actions above a baseline limits learning; and (2) PPO style constraints, such as policy ratio clipping, are not required to improve mathematical reasoning or performance. Building on these insights, we propose REINFORCE with Group Relative Advantage (RGRA), a simplified variant that retains group relative advantage estimation but removes PPO style clipping and policy ratio terms. Experiments across standard mathematical benchmarks indicate that RGRA has the potential to achieve stronger performance than GRPO. Our results suggest that simpler REINFORCE based approaches can effectively enhance reasoning in LLMs, offering a more transparent and efficient alternative to GRPO.

Large Language Models (LLMs) have revolutionized natural language processing, yet aligning these models with human values and preferences using RLHF remains a significant challenge. This challenge is characterized by various instabilities, such as reward hacking and catastrophic forgetting. In this technical report, we propose two innovations to stabilize RLHF training: 1) Advantage Model, which directly models advantage score i.e., extra reward compared to the expected rewards and regulates score distributions across tasks to prevent reward hacking. 2) Selective Rehearsal, which mitigates catastrophic forgetting by strategically selecting data for PPO training and knowledge rehearsing. Our experimental analysis on public and proprietary datasets reveals that the proposed methods not only increase stability in RLHF training but also achieve higher reward scores and win rates.

We initiate the study of Multi-Agent Reinforcement Learning from Human Feedback (MARLHF), exploring both theoretical foundations and empirical validations. We define the task as identifying Nash equilibrium from a preference-only offline dataset in general-sum games, a problem marked by the challenge of sparse feedback signals. Our theory establishes the upper complexity bounds for Nash Equilibrium in effective MARLHF, demonstrating that single-policy coverage is inadequate and highlighting the importance of unilateral dataset coverage. These theoretical insights are verified through comprehensive experiments. To enhance the practical performance, we further introduce two algorithmic techniques. (1) We propose a Mean Squared Error (MSE) regularization along the time axis to achieve a more uniform reward distribution and improve reward learning outcomes. (2) We utilize imitation learning to approximate the reference policy, ensuring stability and effectiveness in training. Our findings underscore the multifaceted approach required for MARLHF, paving the way for effective preference-based multi-agent systems.

Critique-guided reinforcement learning (RL) has emerged as a powerful paradigm for training LLM agents by augmenting sparse outcome rewards with natural-language feedback. However, current methods often rely on static or offline critic models, which fail to adapt as the policy evolves. In on-policy RL, the agent's error patterns shift over time, causing stationary critics to become stale and providing feedback of diminishing utility. To address this, we introduce ECHO (Evolving Critic for Hindsight-Guided Optimization)}, a framework that jointly optimizes the policy and critic through a synchronized co-evolutionary loop. ECHO utilizes a cascaded rollout mechanism where the critic generates multiple diagnoses for an initial trajectory, followed by policy refinement to enable group-structured advantage estimation. We address the challenge of learning plateaus via a saturation-aware gain shaping objective, which rewards the critic for inducing incremental improvements in high-performing trajectories. By employing dual-track GRPO updates, ECHO ensures the critic's feedback stays synchronized with the evolving policy. Experimental results show that ECHO yields more stable training and higher long-horizon task success across open-world environments.

Existing reinforcement learning (RL) methods struggle with long-horizon robotic manipulation tasks, particularly those involving sparse rewards. While action chunking is a promising paradigm for robotic manipulation, using RL to directly learn continuous action chunks in a stable and data-efficient manner remains a critical challenge. This paper introduces AC3 (Actor-Critic for Continuous Chunks), a novel RL framework that learns to generate high-dimensional, continuous action sequences. To make this learning process stable and data-efficient, AC3 incorporates targeted stabilization mechanisms for both the actor and the critic. First, to ensure reliable policy improvement, the actor is trained with an asymmetric update rule, learning exclusively from successful trajectories. Second, to enable effective value learning despite sparse rewards, the critic's update is stabilized using intra-chunk n-step returns and further enriched by a self-supervised module providing intrinsic rewards at anchor points aligned with each action chunk. We conducted extensive experiments on 25 tasks from the BiGym and RLBench benchmarks. Results show that by using only a few demonstrations and a simple model architecture, AC3 achieves superior success rates on most tasks, validating its effective design.

Learning from Demonstration (LfD) aims to facilitate rapid Reinforcement Learning (RL) by leveraging expert demonstrations to pre-train the RL agent. However, the limited availability of expert demonstration data often hinders its ability to effectively aid downstream RL learning. To address this problem, we propose a novel two-stage method dubbed as Skill-enhanced Reinforcement Learning Acceleration (SeRLA). SeRLA introduces a skill-level adversarial Positive-Unlabeled (PU) learning model to extract useful skill prior knowledge by enabling learning from both limited expert data and general low-cost demonstration data in the offline prior learning stage. Subsequently, it deploys a skill-based soft actor-critic algorithm to leverage this acquired prior knowledge in the downstream online RL stage for efficient training of a skill policy network. Moreover, we develop a simple skill-level data enhancement technique to further alleviate data sparsity and improve both skill prior learning and downstream skill policy training. Our experimental results on multiple standard RL environments show the proposed SeRLA method achieves state-of-the-art performance on accelerating reinforcement learning on downstream tasks, especially in the early learning phase.

Multi-step learning applies lookahead over multiple time steps and has proved valuable in policy evaluation settings. However, in the optimal control case, the impact of multi-step learning has been relatively limited despite a number of prior efforts. Fundamentally, this might be because multi-step policy improvements require operations that cannot be approximated by stochastic samples, hence hindering the widespread adoption of such methods in practice. To address such limitations, we introduce doubly multi-step off-policy VI (DoMo-VI), a novel oracle algorithm that combines multi-step policy improvements and policy evaluations. DoMo-VI enjoys guaranteed convergence speed-up to the optimal policy and is applicable in general off-policy learning settings. We then propose doubly multi-step off-policy actor-critic (DoMo-AC), a practical instantiation of the DoMo-VI algorithm. DoMo-AC introduces a bias-variance trade-off that ensures improved policy gradient estimates. When combined with the IMPALA architecture, DoMo-AC has showed improvements over the baseline algorithm on Atari-57 game benchmarks.

While reinforcement learning (RL) shows promise in training tool-use large language models (LLMs) using verifiable outcome rewards, existing methods largely overlook the potential of explicit reasoning rewards to bolster reasoning and tool utilization. Furthermore, natively combining reasoning and outcome rewards may yield suboptimal performance or conflict with the primary optimization objective. To address this, we propose advantage-weighted policy optimization (AWPO) -- a principled RL framework that effectively integrates explicit reasoning rewards to enhance tool-use capability. AWPO incorporates variance-aware gating and difficulty-aware weighting to adaptively modulate advantages from reasoning signals based on group-relative statistics, alongside a tailored clipping mechanism for stable optimization. Extensive experiments demonstrate that AWPO achieves state-of-the-art performance across standard tool-use benchmarks, significantly outperforming strong baselines and leading closed-source models in challenging multi-turn scenarios. Notably, with exceptional parameter efficiency, our 4B model surpasses Grok-4 by 16.0 percent in multi-turn accuracy while preserving generalization capability on the out-of-distribution MMLU-Pro benchmark.

Quality-Diversity algorithms, such as MAP-Elites, are a branch of Evolutionary Computation generating collections of diverse and high-performing solutions, that have been successfully applied to a variety of domains and particularly in evolutionary robotics. However, MAP-Elites performs a divergent search based on random mutations originating from Genetic Algorithms, and thus, is limited to evolving populations of low-dimensional solutions. PGA-MAP-Elites overcomes this limitation by integrating a gradient-based variation operator inspired by Deep Reinforcement Learning which enables the evolution of large neural networks. Although high-performing in many environments, PGA-MAP-Elites fails on several tasks where the convergent search of the gradient-based operator does not direct mutations towards archive-improving solutions. In this work, we present two contributions: (1) we enhance the Policy Gradient variation operator with a descriptor-conditioned critic that improves the archive across the entire descriptor space, (2) we exploit the actor-critic training to learn a descriptor-conditioned policy at no additional cost, distilling the knowledge of the archive into one single versatile policy that can execute the entire range of behaviors contained in the archive. Our algorithm, DCG-MAP-Elites improves the QD score over PGA-MAP-Elites by 82% on average, on a set of challenging locomotion tasks.

We study how vision-language-action (VLA) models can improve through real-world deployments via reinforcement learning (RL). We present a general-purpose method, RL with Experience and Corrections via Advantage-conditioned Policies (RECAP), that provides for RL training of VLAs via advantage conditioning. Our method incorporates heterogeneous data into the self-improvement process, including demonstrations, data from on-policy collection, and expert teleoperated interventions provided during autonomous execution. RECAP starts by pre-training a generalist VLA with offline RL, which we call π^{*}_{0.6}, that can then be specialized to attain high performance on downstream tasks through on-robot data collection. We show that the π^{*}_{0.6} model trained with the full RECAP method can fold laundry in real homes, reliably assemble boxes, and make espresso drinks using a professional espresso machine. On some of the hardest tasks, RECAP more than doubles task throughput and roughly halves the task failure rate.

Large Language Models (LLMs) have made remarkable progress in enhancing step-by-step reasoning through reinforcement learning. However, the Group Relative Policy Optimization (GRPO) algorithm, which relies on sparse reward rules, often encounters the issue of identical rewards within groups, leading to the advantage collapse problem. Existing works typically address this challenge from two perspectives: enforcing model reflection to enhance response diversity, and introducing internal feedback to augment the training signal (advantage). In this work, we begin by analyzing the limitations of model reflection and investigating the policy entropy of responses at the fine-grained sample level. Based on our experimental findings, we propose the EDGE-GRPO algorithm, which adopts Entropy-Driven Advantage and Guided Error Correction to effectively mitigate the problem of advantage collapse. Extensive experiments on several main reasoning benchmarks demonstrate the effectiveness and superiority of our approach. It is available at https://github.com/ZhangXJ199/EDGE-GRPO.

Recent advances in learning decision-making policies can largely be attributed to training expressive policy models, largely via imitation learning. While imitation learning discards non-expert data, reinforcement learning (RL) can still learn from suboptimal data. However, instantiating RL training of a new policy class often presents a different challenge: most deep RL machinery is co-developed with assumptions on the policy class and backbone, resulting in poor performance when the policy class changes. For instance, SAC utilizes a low-variance reparameterization policy gradient for Gaussian policies, but this is unstable for diffusion policies and intractable for autoregressive categorical policies. To address this issue, we develop an offline RL and online fine-tuning approach called policy-agnostic RL (PA-RL) that can effectively train multiple policy classes, with varying architectures and sizes. We build off the basic idea that a universal supervised learning loss can replace the policy improvement step in RL, as long as it is applied on "optimized" actions. To obtain these optimized actions, we first sample multiple actions from a base policy, and run global optimization (i.e., re-ranking multiple action samples using the Q-function) and local optimization (i.e., running gradient steps on an action sample) to maximize the critic on these candidates. PA-RL enables fine-tuning diffusion and transformer policies with either autoregressive tokens or continuous action outputs, at different sizes, entirely via actor-critic RL. Moreover, PA-RL improves the performance and sample-efficiency by up to 2 times compared to existing offline RL and online fine-tuning methods. We show the first result that successfully fine-tunes OpenVLA, a 7B generalist robot policy, autonomously with Cal-QL, an online RL fine-tuning algorithm, improving from 40% to 70% in the real world in 40 minutes.

Reinforcement Learning with Verifiable Rewards (RLVR) elicits long chain-of-thought reasoning in large language models (LLMs), but outcome-based rewards lead to coarse-grained advantage estimation. While existing approaches improve RLVR via token-level entropy or sequence-level length control, they lack a semantically grounded, step-level measure of reasoning progress. As a result, LLMs fail to distinguish necessary deduction from redundant verification: they may continue checking after reaching a correct solution and, in extreme cases, overturn a correct trajectory into an incorrect final answer. To remedy the lack of process supervision, we introduce a training-free probing mechanism that extracts intermediate confidence and correctness and combines them into a Step Potential signal that explicitly estimates the reasoning state at each step. Building on this signal, we propose Step Potential Advantage Estimation (SPAE), a fine-grained credit assignment method that amplifies potential gains, penalizes potential drops, and applies penalty after potential saturates to encourage timely termination. Experiments across multiple benchmarks show SPAE consistently improves accuracy while substantially reducing response length, outperforming strong RL baselines and recent efficient reasoning and token-level advantage estimation methods. The code is available at https://github.com/cii030/SPAE-RL.

This paper develops a policy learning method for tuning a pre-trained policy to adapt to additional tasks without altering the original task. A method named Adaptive Policy Gradient (APG) is proposed in this paper, which combines Bellman's principle of optimality with the policy gradient approach to improve the convergence rate. This paper provides theoretical analysis which guarantees the convergence rate and sample complexity of O(1/T) and O(1/epsilon), respectively, where T denotes the number of iterations and epsilon denotes the accuracy of the resulting stationary policy. Furthermore, several challenging numerical simulations, including cartpole, lunar lander, and robot arm, are provided to show that APG obtains similar performance compared to existing deterministic policy gradient methods while utilizing much less data and converging at a faster rate.

Reinforcement Learning (RL) has emerged as a central paradigm for advancing Large Language Models (LLMs), where pre-training and RL post-training share the same log-likelihood formulation. In contrast, recent RL approaches for diffusion models, most notably Denoising Diffusion Policy Optimization (DDPO), optimize an objective different from the pretraining objectives--score/flow matching loss. In this work, we establish a novel theoretical analysis: DDPO is an implicit form of score/flow matching with noisy targets, which increases variance and slows convergence. Building on this analysis, we introduce Advantage Weighted Matching (AWM), a policy-gradient method for diffusion. It uses the same score/flow-matching loss as pretraining to obtain a lower-variance objective and reweights each sample by its advantage. In effect, AWM raises the influence of high-reward samples and suppresses low-reward ones while keeping the modeling objective identical to pretraining. This unifies pretraining and RL conceptually and practically, is consistent with policy-gradient theory, reduces variance, and yields faster convergence. This simple yet effective design yields substantial benefits: on GenEval, OCR, and PickScore benchmarks, AWM delivers up to a 24times speedup over Flow-GRPO (which builds on DDPO), when applied to Stable Diffusion 3.5 Medium and FLUX, without compromising generation quality. Code is available at https://github.com/scxue/advantage_weighted_matching.

In the context of a short video & live stream mixed recommendation scenario, the live stream recommendation system (RS) decides whether to allocate at most one live stream into the video feed for each user request. To maximize long-term user engagement, it is crucial to determine an optimal live stream policy for accurate live stream allocation. The inappropriate live stream allocation policy can significantly affect the duration of the usage app and user retention, which ignores the long-term negative impact of live stream allocation. Recently, reinforcement learning (RL) has been widely applied in recommendation systems to capture long-term user engagement. However, traditional RL algorithms often face divergence and instability problems, which restricts the application and deployment in the large-scale industrial recommendation systems, especially in the aforementioned challenging scenario. To address these challenges, we propose a novel Supervised Learning-enhanced Multi-Group Actor Critic algorithm (SL-MGAC). Specifically, we introduce a supervised learning-enhanced actor-critic framework that incorporates variance reduction techniques, where multi-task reward learning helps restrict bootstrapping error accumulation during critic learning. Additionally, we design a multi-group state decomposition module for both actor and critic networks to reduce prediction variance and improve model stability. We also propose a novel reward function to prevent overly greedy live stream allocation. Empirically, we evaluate the SL-MGAC algorithm using offline policy evaluation (OPE) and online A/B testing. Experimental results demonstrate that the proposed method not only outperforms baseline methods under the platform-level constraints but also exhibits enhanced stability in online recommendation scenarios.

Risk-sensitive reinforcement learning (RL) has become a popular tool to control the risk of uncertain outcomes and ensure reliable performance in various sequential decision-making problems. While policy gradient methods have been developed for risk-sensitive RL, it remains unclear if these methods enjoy the same global convergence guarantees as in the risk-neutral case. In this paper, we consider a class of dynamic time-consistent risk measures, called Expected Conditional Risk Measures (ECRMs), and derive policy gradient updates for ECRM-based objective functions. Under both constrained direct parameterization and unconstrained softmax parameterization, we provide global convergence and iteration complexities of the corresponding risk-averse policy gradient algorithms. We further test risk-averse variants of REINFORCE and actor-critic algorithms to demonstrate the efficacy of our method and the importance of risk control.

This work presents In-Context Policy Iteration, an algorithm for performing Reinforcement Learning (RL), in-context, using foundation models. While the application of foundation models to RL has received considerable attention, most approaches rely on either (1) the curation of expert demonstrations (either through manual design or task-specific pretraining) or (2) adaptation to the task of interest using gradient methods (either fine-tuning or training of adapter layers). Both of these techniques have drawbacks. Collecting demonstrations is labor-intensive, and algorithms that rely on them do not outperform the experts from which the demonstrations were derived. All gradient techniques are inherently slow, sacrificing the "few-shot" quality that made in-context learning attractive to begin with. In this work, we present an algorithm, ICPI, that learns to perform RL tasks without expert demonstrations or gradients. Instead we present a policy-iteration method in which the prompt content is the entire locus of learning. ICPI iteratively updates the contents of the prompt from which it derives its policy through trial-and-error interaction with an RL environment. In order to eliminate the role of in-weights learning (on which approaches like Decision Transformer rely heavily), we demonstrate our algorithm using Codex, a language model with no prior knowledge of the domains on which we evaluate it.

Methods for controlling large language models (LLMs), including local weight fine-tuning, LoRA-based adaptation, and activation-based interventions, are often studied in isolation, obscuring their connections and making comparison difficult. In this work, we present a unified view that frames these interventions as dynamic weight updates induced by a control signal, placing them within a single conceptual framework. Building on this view, we propose a unified preference-utility analysis that separates control effects into preference, defined as the tendency toward a target concept, and utility, defined as coherent and task-valid generation, and measures both on a shared log-odds scale using polarity-paired contrastive examples. Across methods, we observe a consistent trade-off between preference and utility: stronger control increases preference while predictably reducing utility. We further explain this behavior through an activation manifold perspective, in which control shifts representations along target-concept directions to enhance preference, while utility declines primarily when interventions push representations off the model's valid-generation manifold. Finally, we introduce a new steering approach SPLIT guided by this analysis that improves preference while better preserving utility. Code is available at https://github.com/zjunlp/EasyEdit/blob/main/examples/SPLIT.md.

Group Relative Policy Optimization (GRPO) assigns a single scalar advantage to all tokens in a completion. For structured generations with explicit segments and objectives, this couples unrelated reward signals across segments, leading to objective interference and misattributed credit. We propose Blockwise Advantage Estimation, a family of GRPO-compatible methods that assigns each objective its own advantage and applies it only to the tokens in the corresponding text block, reducing reliance on hand-designed scalar rewards and scaling naturally to additional objectives. A key challenge is estimating advantages for later blocks whose rewards are conditioned on sampled prefixes; standard unbiased approaches require expensive nested rollouts from intermediate states. Concretely, we introduce an Outcome-Conditioned Baseline that approximates intermediate state values using only within-group statistics by stratifying samples according to a prefix-derived intermediate outcome. On math tasks with uncertainty estimation, our method mitigates reward interference, is competitive with a state-of-the-art reward-designed approach, and preserves test-time gains from confidence-weighted ensembling. More broadly, it provides a modular recipe for optimizing sequential objectives in structured generations without additional rollouts.

Meta-gradient Reinforcement Learning (RL) allows agents to self-tune their hyper-parameters in an online fashion during training. In this paper, we identify a bias in the meta-gradient of current meta-gradient RL approaches. This bias comes from using the critic that is trained using the meta-learned discount factor for the advantage estimation in the outer objective which requires a different discount factor. Because the meta-learned discount factor is typically lower than the one used in the outer objective, the resulting bias can cause the meta-gradient to favor myopic policies. We propose a simple solution to this issue: we eliminate this bias by using an alternative, outer value function in the estimation of the outer loss. To obtain this outer value function we add a second head to the critic network and train it alongside the classic critic, using the outer loss discount factor. On an illustrative toy problem, we show that the bias can cause catastrophic failure of current meta-gradient RL approaches, and show that our proposed solution fixes it. We then apply our method to a more complex environment and demonstrate that fixing the meta-gradient bias can significantly improve performance.

The Reinforcement Learning (RL) building blocks, i.e. Q-functions and policy networks, usually take elements from the cartesian product of two domains as input. In particular, the input of the Q-function is both the state and the action, and in multi-task problems (Meta-RL) the policy can take a state and a context. Standard architectures tend to ignore these variables' underlying interpretations and simply concatenate their features into a single vector. In this work, we argue that this choice may lead to poor gradient estimation in actor-critic algorithms and high variance learning steps in Meta-RL algorithms. To consider the interaction between the input variables, we suggest using a Hypernetwork architecture where a primary network determines the weights of a conditional dynamic network. We show that this approach improves the gradient approximation and reduces the learning step variance, which both accelerates learning and improves the final performance. We demonstrate a consistent improvement across different locomotion tasks and different algorithms both in RL (TD3 and SAC) and in Meta-RL (MAML and PEARL).

Reinforcement Learning with Verifiable Rewards (RLVR) is a powerful paradigm for enhancing the reasoning ability of Large Language Models (LLMs). Yet current RLVR methods often explore poorly, leading to premature convergence and entropy collapse. To address this challenge, we introduce Curiosity-Driven Exploration (CDE), a framework that leverages the model's own intrinsic sense of curiosity to guide exploration. We formalize curiosity with signals from both the actor and the critic: for the actor, we use perplexity over its generated response, and for the critic, we use the variance of value estimates from a multi-head architecture. Both signals serve as an exploration bonus within the RLVR framework to guide the model. Our theoretical analysis shows that the actor-wise bonus inherently penalizes overconfident errors and promotes diversity among correct responses; moreover, we connect the critic-wise bonus to the well-established count-based exploration bonus in RL. Empirically, our method achieves an approximate +3 point improvement over standard RLVR using GRPO/PPO on AIME benchmarks. Further analysis identifies a calibration collapse mechanism within RLVR, shedding light on common LLM failure modes.

Model-based representations recently stand out as a promising framework that embeds latent dynamics information into the representations for downstream off-policy actor-critic learning. It implicitly combines the advantages of both model-free and model-based approaches while avoiding the training costs associated with model-based methods. Nevertheless, existing model-based representation methods can fail to capture sufficient information about relevant variables and can overfit to early experiences in the replay buffer. These incur biases in representation and actor-critic learning, leading to inferior performance. To address this, we propose Debiased model-based Representations for Q-learning, tagged DR.Q algorithm. DR.Q explicitly maximizes the mutual information between the representations of the current state-action pair and the next state besides minimizing their deviations, and samples transitions with faded prioritized experience replay. We evaluate DR.Q on numerous continuous control benchmarks with a single set of hyperparameters, and the results demonstrate that DR.Q can match or surpass recent strong baselines, sometimes outperforming them by a large margin. Our code is available at https://github.com/dmksjfl/DR.Q.

Large Language Model agents have rapidly evolved from static text generators into dynamic systems capable of executing complex autonomous workflows. To enhance reliability, multi-agent frameworks assigning specialized roles are increasingly adopted to enable self-reflection and mutual auditing. While such role-playing effectively leverages domain expert knowledge, we find it simultaneously induces a human-like cognitive bias known as Actor-Observer Asymmetry (AOA). Specifically, an agent acting as an actor (during self-reflection) tends to attribute failures to external factors, whereas an observer (during mutual auditing) attributes the same errors to internal faults. We quantify this using our new Ambiguous Failure Benchmark, which reveals that simply swapping perspectives triggers the AOA effect in over 20% of cases for most models. To tame this bias, we introduce ReTAS (Reasoning via Thesis-Antithesis-Synthesis), a model trained through dialectical alignment to enforce perspective-invariant reasoning. By integrating dialectical chain-of-thought with Group Relative Policy Optimization, ReTAS guides agents to synthesize conflicting viewpoints into an objective consensus. Experiments demonstrate that ReTAS effectively mitigates attribution inconsistency and significantly improves fault resolution rates in ambiguous scenarios.

Reinforcement Learning (RL) has emerged as a powerful paradigm for training LLM-based agents, yet remains limited by low sample efficiency, stemming not only from sparse outcome feedback but also from the agent's inability to leverage prior experience across episodes. While augmenting agents with historical experience offers a promising remedy, existing approaches suffer from a critical weakness: the experience distilled from history is either stored statically or fail to coevolve with the improving actor, causing a progressive misalignment between the experience and the actor's evolving capability that diminishes its utility over the course of training. Inspired by complementary learning systems in neuroscience, we present Complementary RL to achieve seamless co-evolution of an experience extractor and a policy actor within the RL optimization loop. Specifically, the actor is optimized via sparse outcome-based rewards, while the experience extractor is optimized according to whether its distilled experiences demonstrably contribute to the actor's success, thereby evolving its experience management strategy in lockstep with the actor's growing capabilities. Empirically, Complementary RL outperforms outcome-based agentic RL baselines that do not learn from experience, achieving 10% performance improvement in single-task scenarios and exhibits robust scalability in multi-task settings. These results establish Complementary RL as a paradigm for efficient experience-driven agent learning.

Reinforcement Learning from Human Feedback (RLHF) is currently the most widely used method to align large language models (LLMs) with human preferences. Existing RLHF methods can be roughly categorized as either reward-based or reward-free. Novel applications such as ChatGPT and Claude leverage reward-based methods that first learn a reward model and apply actor-critic algorithms, such as Proximal Policy Optimization (PPO). However, in academic benchmarks, state-of-the-art results are often achieved via reward-free methods, such as Direct Preference Optimization (DPO). Is DPO truly superior to PPO? Why does PPO perform poorly on these benchmarks? In this paper, we first conduct both theoretical and empirical studies on the algorithmic properties of DPO and show that DPO may have fundamental limitations. Moreover, we also comprehensively examine PPO and reveal the key factors for the best performances of PPO in fine-tuning LLMs. Finally, we benchmark DPO and PPO across various a collection of RLHF testbeds, ranging from dialogue to code generation. Experiment results demonstrate that PPO is able to surpass other alignment methods in all cases and achieve state-of-the-art results in challenging code competitions.

Neural architecture search (NAS) has achieved remarkable results in deep neural network design. Differentiable architecture search converts the search over discrete architectures into a hyperparameter optimization problem which can be solved by gradient descent. However, questions have been raised regarding the effectiveness and generalizability of gradient methods for solving non-convex architecture hyperparameter optimization problems. In this paper, we propose L^{2}NAS, which learns to intelligently optimize and update architecture hyperparameters via an actor neural network based on the distribution of high-performing architectures in the search history. We introduce a quantile-driven training procedure which efficiently trains L^{2}NAS in an actor-critic framework via continuous-action reinforcement learning. Experiments show that L^{2}NAS achieves state-of-the-art results on NAS-Bench-201 benchmark as well as DARTS search space and Once-for-All MobileNetV3 search space. We also show that search policies generated by L^{2}NAS are generalizable and transferable across different training datasets with minimal fine-tuning.

In reinforcement learning (RL), function approximation errors are known to easily lead to the Q-value overestimations, thus greatly reducing policy performance. This paper presents a distributional soft actor-critic (DSAC) algorithm, which is an off-policy RL method for continuous control setting, to improve the policy performance by mitigating Q-value overestimations. We first discover in theory that learning a distribution function of state-action returns can effectively mitigate Q-value overestimations because it is capable of adaptively adjusting the update stepsize of the Q-value function. Then, a distributional soft policy iteration (DSPI) framework is developed by embedding the return distribution function into maximum entropy RL. Finally, we present a deep off-policy actor-critic variant of DSPI, called DSAC, which directly learns a continuous return distribution by keeping the variance of the state-action returns within a reasonable range to address exploding and vanishing gradient problems. We evaluate DSAC on the suite of MuJoCo continuous control tasks, achieving the state-of-the-art performance.

Hybrid RL is the setting where an RL agent has access to both offline data and online data by interacting with the real-world environment. In this work, we propose a new hybrid RL algorithm that combines an on-policy actor-critic method with offline data. On-policy methods such as policy gradient and natural policy gradient (NPG) have shown to be more robust to model misspecification, though sometimes it may not be as sample efficient as methods that rely on off-policy learning. On the other hand, offline methods that depend on off-policy training often require strong assumptions in theory and are less stable to train in practice. Our new approach integrates a procedure of off-policy training on the offline data into an on-policy NPG framework. We show that our approach, in theory, can obtain a best-of-both-worlds type of result -- it achieves the state-of-art theoretical guarantees of offline RL when offline RL-specific assumptions hold, while at the same time maintaining the theoretical guarantees of on-policy NPG regardless of the offline RL assumptions' validity. Experimentally, in challenging rich-observation environments, we show that our approach outperforms a state-of-the-art hybrid RL baseline which only relies on off-policy policy optimization, demonstrating the empirical benefit of combining on-policy and off-policy learning. Our code is publicly available at https://github.com/YifeiZhou02/HNPG.

Temporal-difference (TD) methods learn state and action values efficiently by bootstrapping from their own future value predictions, but such a self-bootstrapping mechanism is prone to bootstrapping bias, where the errors in the value targets accumulate across steps and result in biased value estimates. Recent work has proposed to use chunked critics, which estimate the value of short action sequences ("chunks") rather than individual actions, speeding up value backup. However, extracting policies from chunked critics is challenging: policies must output the entire action chunk open-loop, which can be sub-optimal for environments that require policy reactivity and also challenging to model especially when the chunk length grows. Our key insight is to decouple the chunk length of the critic from that of the policy, allowing the policy to operate over shorter action chunks. We propose a novel algorithm that achieves this by optimizing the policy against a distilled critic for partial action chunks, constructed by optimistically backing up from the original chunked critic to approximate the maximum value achievable when a partial action chunk is extended to a complete one. This design retains the benefits of multi-step value propagation while sidestepping both the open-loop sub-optimality and the difficulty of learning action chunking policies for long action chunks. We evaluate our method on challenging, long-horizon offline goal-conditioned tasks and show that it reliably outperforms prior methods. Code: github.com/ColinQiyangLi/dqc.

Reinforcement learning fine-tuning (RLFT) is a dominant paradigm for improving pretrained policies for downstream tasks. These pretrained policies, trained on large datasets, produce generations with a broad range of promising but unrefined behaviors. Often, a critical failure mode of RLFT arises when policies lose this diversity and collapse into a handful of easily exploitable outputs. This convergence hinders exploration, which is essential for expanding the capabilities of the pretrained policy and for amplifying the benefits of test-time compute scaling. To address this, we introduce an objective for policy gradient methods that explicitly enforces the exploration and refinement of diverse generations, which we call a polychromic objective. We then show how proximal policy optimization (PPO) can be adapted to optimize this objective. Our method (1) employs vine sampling to collect on-policy rollouts and (2) modifies the advantage function to reflect the advantage under our new objective. Experiments on BabyAI, Minigrid, and Algorithmic Creativity show that our method improves success rates by reliably solving a larger set of environment configurations and generalizes better under large perturbations. Moreover, when given multiple attempts in pass@k experiments, the policy achieves substantially higher coverage, demonstrating its ability to maintain and exploit a diverse repertoire of strategies.

As agentic AI becomes more widespread, agents with distinct and possibly conflicting goals will interact in complex ways. These multi-agent interactions pose a fundamental challenge, particularly in social dilemmas, where agents' individual incentives can undermine collective welfare. While reinforcement learning (RL) has been effective for aligning large language models (LLMs) in the single-agent regime, prior small-network results suggest that standard RL in multi-agent settings often converges to defecting, self-interested policies. We show the same effect in LLMs: despite cooperative priors, RL-trained LLM agents develop opportunistic behavior that can exploit even advanced closed-source models. To address this tendency of RL to converge to poor equilibria, we adapt a recent opponent-learning awareness algorithm, Advantage Alignment, to fine-tune LLMs toward multi-agent cooperation and non-exploitability. We then introduce a group-relative baseline that simplifies advantage computation in iterated games, enabling multi-agent training at LLM scale. We also contribute a novel social dilemma environment, Trust-and-Split, which requires natural language communication to achieve high collective welfare. Across a wide range of social dilemmas, policies learned with Advantage Alignment achieve higher collective payoffs while remaining robust against exploitation by greedy agents. We release all of our code to support future work on multi-agent RL training for LLMs.

A major challenge in Reinforcement Learning (RL) is the difficulty of learning an optimal policy from sparse rewards. Prior works enhance online RL with conventional Imitation Learning (IL) via a handcrafted auxiliary objective, at the cost of restricting the RL policy to be sub-optimal when the offline data is generated by a non-expert policy. Instead, to better leverage valuable information in offline data, we develop Generalized Imitation Learning from Demonstration (GILD), which meta-learns an objective that distills knowledge from offline data and instills intrinsic motivation towards the optimal policy. Distinct from prior works that are exclusive to a specific RL algorithm, GILD is a flexible module intended for diverse vanilla off-policy RL algorithms. In addition, GILD introduces no domain-specific hyperparameter and minimal increase in computational cost. In four challenging MuJoCo tasks with sparse rewards, we show that three RL algorithms enhanced with GILD significantly outperform state-of-the-art methods.

When deploying artificial agents in real-world environments where they interact with humans, it is crucial that their behavior is aligned with the values, social norms or other requirements of that environment. However, many environments have implicit constraints that are difficult to specify and transfer to a learning agent. To address this challenge, we propose a novel method that utilizes the principle of maximum causal entropy to learn constraints and an optimal policy that adheres to these constraints, using demonstrations of agents that abide by the constraints. We prove convergence in a tabular setting and provide an approximation which scales to complex environments. We evaluate the effectiveness of the learned policy by assessing the reward received and the number of constraint violations, and we evaluate the learned cost function based on its transferability to other agents. Our method has been shown to outperform state-of-the-art approaches across a variety of tasks and environments, and it is able to handle problems with stochastic dynamics and a continuous state-action space.

Group-based reinforcement learning (RL), such as GRPO, has advanced the capabilities of large language models on long-horizon agentic tasks. To enable more fine-grained policy updates, recent research has increasingly shifted toward stepwise group-based policy optimization, which treats each step in a rollout trajectory independently while using a memory module to retain historical context. However, we find a key issue in estimating stepwise relative advantages, namely context inconsistency, where steps within the same group may differ in their historical contexts. Empirically, we reveal that this issue can lead to severely biased advantage estimation, thereby degrading policy optimization significantly. To address the issue, in this paper, we propose Hierarchy-of-Groups Policy Optimization (HGPO) for long-horizon agentic tasks. Specifically, within a group of rollout trajectories, HGPO assigns each step to multiple hierarchical groups according to the consistency of historical contexts. Then, for each step, HGPO computes distinct advantages within each group and aggregates them with an adaptive weighting scheme. In this way, HGPO can achieve a favorable bias-variance trade-off in stepwise advantage estimation, without extra models or rollouts. Evaluations on two challenging agentic tasks, ALFWorld and WebShop with Qwen2.5-1.5B-Instruct and Qwen2.5-7B-Instruct, show that HGPO significantly outperforms existing agentic RL methods under the same computational constraints. Code is available at https://github.com/langfengQ/verl-agent/tree/master/recipe/hgpo.

Optimization (PPO) has been positioned by recent literature as the canonical method for the RL part of RLHF. PPO performs well empirically but has a heuristic motivation and handles the KL-divergence constraint used in LM-RLHF in an ad-hoc manner and suffers form reward oscillations, entropy collapse, value function drift, and sudden policy divergence that require frequent restarts and extensive hyperparameter tuning. In this paper, we develop a new pure on policy actor-critic RL method for the LM-RLHF setting. We present SAFE (Stable Alignment Finetuning with Entropy-aware control),a novel RLHF algorithm that combines a Double Soft-Min Critic for pessimistic value estimation with a new multi-layer stabilization framework combining entropy-gated KL regulation, and PID-controlled adaptive thresholds. Unlike standard PPO's symmetric KL penalties, SAFE distinguishes high-entropy exploration from low-entropy mode collapse and adjusts penalties dynamically based on reward velocity. Experiments on a 3B parameter model show SAFE achieves +5.15\% training-average reward than PPO (0.725 vs 0.689), negligible reward crashes, and superior KL control than ppo . Our method adds minimal computational overhead and provides an interpretable, crash-resistant RLHF framework that maintains aggressive learning speed while ensuring stable long-horizon optimization suitable for production deployment. Code is available at https://github.com/ryyzn9/SAFE

We study the adaption of Soft Actor-Critic (SAC), which is considered as a state-of-the-art reinforcement learning (RL) algorithm, from continuous action space to discrete action space. We revisit vanilla discrete SAC and provide an in-depth understanding of its Q value underestimation and performance instability issues when applied to discrete settings. We thereby propose Stable Discrete SAC (SDSAC), an algorithm that leverages entropy-penalty and double average Q-learning with Q-clip to address these issues. Extensive experiments on typical benchmarks with discrete action space, including Atari games and a large-scale MOBA game, show the efficacy of our proposed method. Our code is at: https://github.com/coldsummerday/SD-SAC.git.

Standard policy gradients weight each sampled action by advantage alone, regardless of how likely that action was under the current policy. This creates two pathologies: within a single decision context (e.g. one image or prompt), a rare negative-advantage action can disproportionately distort the update direction; across many such contexts in a batch, the expected gradient over-allocates budget to contexts the policy already handles well. We introduce the Delightful Policy Gradient (DG), which gates each term with a sigmoid of delight, the product of advantage and action surprisal (negative log-probability). For K-armed bandits, DG provably improves directional accuracy in a single context and, across multiple contexts, shifts the expected gradient strictly closer to the supervised cross-entropy oracle. This second effect is not variance reduction: it persists even with infinite samples. Empirically, DG outperforms REINFORCE, PPO, and advantage-weighted baselines across MNIST, transformer sequence modeling, and continuous control, with larger gains on harder tasks.

Training large language models (LLMs) to spend more time thinking and reflection before responding is crucial for effectively solving complex reasoning tasks in fields such as science, coding, and mathematics. However, the effectiveness of mechanisms like self-reflection and self-correction depends on the model's capacity to accurately assess its own performance, which can be limited by factors such as initial accuracy, question difficulty, and the lack of external feedback. In this paper, we delve into a two-player paradigm that separates the roles of reasoning and critique models, where the critique model provides step-level feedback to supervise the reasoning (actor) model during both test-time and train-time. We first propose AutoMathCritique, an automated and scalable framework for collecting critique data, resulting in a dataset of 76,321 responses paired with step-level feedback. Fine-tuning language models with this dataset enables them to generate natural language feedback for mathematical reasoning. We demonstrate that the critique models consistently improve the actor's performance on difficult queries at test-time, especially when scaling up inference-time computation. Motivated by these findings, we introduce the critique-based supervision to the actor's self-training process, and propose a critique-in-the-loop self-improvement method. Experiments show that the method improves the actor's exploration efficiency and solution diversity, especially on challenging queries, leading to a stronger reasoning model. Lastly, we take the preliminary step to explore training self-talk reasoning models via critique supervision and showcase its potential. Our code and datasets are at https://mathcritique.github.io/{https://mathcritique.github.io/}.

We propose a novel approach to addressing two fundamental challenges in Model-based Reinforcement Learning (MBRL): the computational expense of repeatedly finding a good policy in the learned model, and the objective mismatch between model fitting and policy computation. Our "lazy" method leverages a novel unified objective, Performance Difference via Advantage in Model, to capture the performance difference between the learned policy and expert policy under the true dynamics. This objective demonstrates that optimizing the expected policy advantage in the learned model under an exploration distribution is sufficient for policy computation, resulting in a significant boost in computational efficiency compared to traditional planning methods. Additionally, the unified objective uses a value moment matching term for model fitting, which is aligned with the model's usage during policy computation. We present two no-regret algorithms to optimize the proposed objective, and demonstrate their statistical and computational gains compared to existing MBRL methods through simulated benchmarks.

Policy gradient methods are an appealing approach in reinforcement learning because they directly optimize the cumulative reward and can straightforwardly be used with nonlinear function approximators such as neural networks. The two main challenges are the large number of samples typically required, and the difficulty of obtaining stable and steady improvement despite the nonstationarity of the incoming data. We address the first challenge by using value functions to substantially reduce the variance of policy gradient estimates at the cost of some bias, with an exponentially-weighted estimator of the advantage function that is analogous to TD(lambda). We address the second challenge by using trust region optimization procedure for both the policy and the value function, which are represented by neural networks. Our approach yields strong empirical results on highly challenging 3D locomotion tasks, learning running gaits for bipedal and quadrupedal simulated robots, and learning a policy for getting the biped to stand up from starting out lying on the ground. In contrast to a body of prior work that uses hand-crafted policy representations, our neural network policies map directly from raw kinematics to joint torques. Our algorithm is fully model-free, and the amount of simulated experience required for the learning tasks on 3D bipeds corresponds to 1-2 weeks of real time.

Interactive multimodal agents must convert raw visual observations into coherent sequences of language-conditioned actions -- a capability that current vision-language models (VLMs) still lack. Earlier reinforcement-learning (RL) efforts could, in principle, endow VLMs with such skills, but they have seldom tested whether the learned behaviours generalize beyond their training simulators, and they depend either on brittle hyperparameter tuning or on dense-reward environments with low state variability. We introduce Vision-Language Decoupled Actor-Critic (VL-DAC), a lightweight, hyperparameter-free RL algorithm. VL-DAC applies PPO updates to action tokens while learning value only at the environment-step level: an arrangement, to our knowledge, not previously explored for large VLMs or LLMs. This simple decoupling removes unstable weighting terms and yields faster, more reliable convergence. Training a single VLM with VL-DAC in one inexpensive simulator at a time (MiniWorld, Gym-Cards, ALFWorld, or WebShop) already produces policies that generalize widely: +50\% relative on BALROG (game-centric agentic control), +5\% relative on the hardest part of VSI-Bench (spatial planning), and +2\% on VisualWebBench (web navigation), all without degrading general image understanding accuracy. These results provide the first evidence that a simple RL algorithm can train VLMs entirely in cheap synthetic worlds while delivering measurable gains on real-image agentic, spatial-reasoning, and web-navigation benchmarks.

Large reasoning models improve with more test-time computation, but often overthink, producing unnecessarily long chains-of-thought that raise cost without improving accuracy. Prior reinforcement learning approaches typically rely on a single outcome reward with trajectory-level length penalties, which cannot distinguish essential from redundant reasoning steps and therefore yield blunt compression. Although recent work incorporates step-level signals, such as offline pruning, supervised data construction, or verifier-based intermediate rewards, reasoning length is rarely treated as an explicit step-level optimization objective during RL. We propose Step-wise Adaptive Penalization (SWAP), a fine-grained framework that allocates length reduction across steps based on intrinsic contribution. We estimate step importance from the model's on-policy log-probability improvement toward the correct answer, then treat excess length as a penalty mass redistributed to penalize low-importance steps more heavily while preserving high-importance reasoning. We optimize with a unified outcome-process advantage within group-relative policy optimization. Extensive experiments demonstrate that SWAP reduces reasoning length by 64.3% on average while improving accuracy by 5.7% relative to the base model.

Deep reinforcement learning (DRL) has successfully solved various problems recently, typically with a unimodal policy representation. However, grasping distinguishable skills for some tasks with non-unique optima can be essential for further improving its learning efficiency and performance, which may lead to a multimodal policy represented as a mixture-of-experts (MOE). To our best knowledge, present DRL algorithms for general utility do not deploy this method as policy function approximators due to the potential challenge in its differentiability for policy learning. In this work, we propose a probabilistic mixture-of-experts (PMOE) implemented with a Gaussian mixture model (GMM) for multimodal policy, together with a novel gradient estimator for the indifferentiability problem, which can be applied in generic off-policy and on-policy DRL algorithms using stochastic policies, e.g., Soft Actor-Critic (SAC) and Proximal Policy Optimisation (PPO). Experimental results testify the advantage of our method over unimodal polices and two different MOE methods, as well as a method of option frameworks, based on the above two types of DRL algorithms, on six MuJoCo tasks. Different gradient estimations for GMM like the reparameterisation trick (Gumbel-Softmax) and the score-ratio trick are also compared with our method. We further empirically demonstrate the distinguishable primitives learned with PMOE and show the benefits of our method in terms of exploration.