Neural machine translation Kalchbrenner and Blunsom (2013); Sutskever et al. (2014); Cho et al. (2014); Bahdanau et al. (2014) which directly leverages a single neural network to transform the source sentence into the target sentence, has drawn more and more attention in both academia and industry Shen et al. (2015); Wu et al. (2016); Johnson et al. (2016); Gehring et al. (2017); Vaswani et al. (2017). This end-to-end NMT typically consists of two sub neural networks. The encoder network reads and encodes the source sentence into the context vector representation; and the decoder network generates the target sentence word by word based on the context vector. To dynamically generate a context vector for a target word being generated, the attention mechanism which enables the model to focus on the relevant words in the source-side sentence is usually deployed. Under the encoder-decoder framework, many variants of the model structure, such as convolutional neural network (CNN) and recurrent neural network (RNN) are proposed Bahdanau et al. (2014); Gehring et al. (2017). Recently, Gehring et al. (2017) propose the Transformer, the first sequence transduction model based entirely on attention, achieving state-of-the-art performance on the English-German and English-French translation tasks. Despite its success, the Transformer, similar to traditional NMT models, is still optimized to maximize the likelihood estimation of the ground word (MLE) at each time step. Such an objective poses a hidden danger to NMT models. That is, the model may generate the best candidate word for the current time step yet a bad component of the whole sentence in the long run. Minimum risk training (MRT) Shen et al. (2015) is proposed to alleviate such a limitation by adopting the sequence level objective, i.e., the sentence-level BLEU, for traditional NMT models. Yet somewhat improved, this objective still does not guarantee the translation results to be natural and sufficient. Since the BLEU point is computed as the geometric mean of the modified n-gram precisions Papineni et al. (2002), almost all of the existing objectives essentially train NMT models to generate sentences with n-gram precisions as high as possible (MLE can be viewed to generate sentences with high 1-gram precisions). While n-gram precisions largely tell the good sentence apart from the bad one, it is widely acknowledged that higher n-gram precisions do not guarantee better sentences Callison-Burch and Osborne (2006); Chatterjee et al. (2007). Additionally, the manually defined objective, i.e., the n-gram precision, is unable to cover all crucial aspects of the data distribution and NMT models may be trained to generate suboptimal sentences Luc et al. (2016)111This paper has been accepted by NAACL-HLT2018..

In this paper, to address the limitation mentioned above, we borrow the idea of generative adversarial training from computer vision Goodfellow et al. (2014); Denton et al. (2015) to directly train the NMT model generating sentences which are hard to be discriminated from human translations. The motivation behind is that while we can not manually define the data distribution of golden sentences comprehensively, we are able to utilize a discriminative network to learn automatically what the golden sentences look like. Following this motivation, we build a conditional sequence generative adversarial net where we jointly train two sub adversarial models: A generator generates the target-language sentence based on the input source-language sentence; And a discriminator, conditioned on the source-language sentence, predicts the probability of the target-language sentence being a human-generated one. During the training process, the generator aims to fool the discriminator into believing that its output is a human-generated sentence, and the discriminator makes efforts not to be fooled by improving its ability to distinguish the machine-generated sentence from the human-generated one. This kind of adversarial training achieves a win-win situation when the generator and discriminator reach a Nash Equilibrium Zhao et al. (2016); Arora et al. (2017); Guimaraes et al. (2017). Besides generating the desired distribution, we also want to directly guide the generator with a static and specific objective, such as generating sentences with high BLEU points. To this end, the smoothed sentence-level BLEU Nakov et al. (2012) is utilized as the reinforced objective for the generator. During training, we employ both the dynamic discriminator and the static BLEU objective to evaluate the generated sentences and feedback the evaluations to guide the learning of the generator. In summary, we mainly make the following contributions:•To the best of our knowledge, this work is among the first endeavors to introduce the generative adversarial training into NMT. We directly train the NMT model to generate sentences which are hard to be discriminated from human translations. The proposed model can be applied to any end-to-end NMT systems.•We conduct extensive experiments on English-German and Chinese-English translation tasks and we test two different NMT models, the traditional RNNSearch Bahdanau et al. (2014) and the state-of-the-art Transformer. Experimental results show that the proposed approach consistently achieves great success.•Last but not least, we propose the smoothed sentence-level BLEU as the static and specific objective for the generator which biases the generation towards achieving high BLEU points. We show that the proposed approach is a weighted combination of the naive GAN and MRT.

The RNNSearch is the traditional NMT model which has been widely explored. We follow the de facto standard implementation by Bahdanau et al. (2014). The encoder is a bidirectional gated recurrent units that encodes the input sequence x=(x1,…,xm)𝑥subscript𝑥1…subscript𝑥𝑚x=(x_{1},\ldots,x_{m}) and calculates the forward sequence of hidden states (h1→,…,hm→)→subscriptℎ1…→subscriptℎ𝑚(\overrightarrow{h_{1}},\ldots,\overrightarrow{h_{m}}), and a backward sequence of hidden states (h1←,…,hm←)←subscriptℎ1…←subscriptℎ𝑚(\overleftarrow{h_{1}},\ldots,\overleftarrow{h_{m}}). The final annotation vector hjsubscriptℎ𝑗h_{j} is calculated by concatenating hj→→subscriptℎ𝑗\overrightarrow{h_{j}} and hj←←subscriptℎ𝑗\overleftarrow{h_{j}}. The decoder is a recurrent neural network that predicts a target sequence y=(y1,…,yn)𝑦subscript𝑦1…subscript𝑦𝑛y=(y_{1},\ldots,y_{n}). Each word yisubscript𝑦𝑖y_{i} is predicted on a recurrent hidden state sisubscript𝑠𝑖s_{i}, the previously predicted word yi−1subscript𝑦𝑖1y_{i-1} and a context vector cisubscript𝑐𝑖c_{i}. The cisubscript𝑐𝑖c_{i} is computed as a weighted sum of the encoded annotations hjsubscriptℎ𝑗h_{j}. The weight ai​jsubscript𝑎𝑖𝑗a_{ij} of each annotation hjsubscriptℎ𝑗h_{j} is computed by the attention mechanism, which models the alignment between yisubscript𝑦𝑖y_{i} and xjsubscript𝑥𝑗x_{j}.

The Transformer, recently proposed by Vaswani et al. (2017), achieves state-of-the-art results on both WMT2014 English-German and WMT2014 English-French translation tasks. The encoder of Transformer is composed of a stack of six identical layers. Each layer consists of a multi-head self-attention and a simple position-wise fully connected feed-forward network. The decoder is also composed of a stack of six identical layers. In addition to the two sub-layers in each encoder layer, the decoder inserts a third sub-layer, which performs multi-head attention over the output of the encoder stack. The Transformer can be trained significantly faster than architectures based on recurrent or convolutional layers since it allows for significantly more parallelization.

Generative adversarial network, has enjoyed great success in computer vision and has been widely applied to image generation Zhu et al. (2017); Radford et al. (2015). The conditional generative adversarial nets Gauthier (2014) apply an extension of generative adversarial network to a conditional setting, which enables the networks to condition on some arbitrary external data. Some recent works have begun to apply the generative adversarial training into the NLP area: Chen et al. (2016) apply the idea of generative adversarial training to sentiment analysis and Zhang et al. (2017) use the idea to domain adaptation tasks. For sequence generation problem, Yu et al. (2016) leverage policy gradient reinforcement learning to back-propagate the reward from the discriminator, showing presentable results for poem generation, speech language generation and music generation. Similarly, Zhang et al. (2016) generate the text from random noise via adversarial training. A striking difference from the works mentioned above is that, our work is in the conditional setting where the target-language sentence is generated conditioned on the source-language one. In parallel to our work, Li et al. (2017) propose a similar conditional sequence generative adversarial training for dialogue generation. They use a hierarchical long-short term memory (LSTM) architecture for the discriminator. In contrast to their approach, we apply the CNN-based discriminator for the machine translation task. Furthermore, we propose to utilize the sentence-level BLEU as the specific objective for the generator. Detailed training strategies for the proposed model and extensive quantitative results are reported. We noticed that Wu et al. (2017) is exploring the potential of GAN in NMT too. There are some differences in training strategies and experimental settings between Wu et al. (2017) and this work. And the most significant difference is that we propose a novel BLEU-reinforced GAN for NMT.

In this section, we describe the architecture of the proposed BLEU reinforced conditional sequence generative adversarial net (referred to as BR-CSGAN) in detail. The sentence generation process is viewed as a sequence of actions that are taken according to a policy regulated by the generator. In this work, we take the policy gradient training strategies following Yu et al. (2016). The whole architecture of the proposed model is depicted in figure 1. The model mainly consists of three sub modules:

Generator Based on the source-language sentences, the generator G aims to generate target-language sentences indistinguishable from human translations.

Discriminator The discriminator D, conditioned on the source-language sentences, tries to distinguish the machine-generated sentences from human translations. D can be viewed as a dynamic objective since it is updated synchronously with G.

BLEU objective The sentence-level BLEU Q serves as the reinforced objective, guiding the generation towards high BLEU points. Q is a static function which will not be updated during training.

Resembling NMT models, the generator G defines the policy that generates the target sentence y𝑦y given the source sentence x𝑥x. The generator takes exactly the same architecture with NMT models. Note that we do not assume the specific architecture of the generator. To verify the effectiveness of the proposed method, we take two different architectures for the generator, the RNNSearch 222https://github.com/nyu-dl/dl4mt-tutorial and Transformer 333https://github.com/tensorflow/tensor2tensor.

Recently, the deep discriminative models such as the CNN and RNN have shown a high performance in complicated sequence classification tasks. Here, the discriminator is implemented based on the CNN architecture.

Since sentences generated by the generator have variable lengths, the CNN padding is used to transform the sentences to sequences with fixed length T𝑇T, which is the maximum length set for the output of the generator. Given the source-language sequence x1,…,xTsubscript𝑥1…subscript𝑥𝑇x_{1},\ldots,x_{T} and target-language sequence y1,…,yTsubscript𝑦1…subscript𝑦𝑇y_{1},\ldots,y_{T}, we build the source matrix X1:Tsubscript𝑋:1𝑇X_{1:T} and target matrix Y1:Tsubscript𝑌:1𝑇Y_{1:T} respectively as:X1:T=x1;x2;…;xTsubscript𝑋:1𝑇subscript𝑥1subscript𝑥2…subscript𝑥𝑇X_{1:T}=x_{1};x_{2};\ldots;x_{T}(1)andY1:T=y1;y2;…;yTsubscript𝑌:1𝑇subscript𝑦1subscript𝑦2…subscript𝑦𝑇Y_{1:T}=y_{1};y_{2};\ldots;y_{T}(2)where xtsubscript𝑥𝑡x_{t}, yt∈Rksubscript𝑦𝑡superscript𝑅𝑘y_{t}\in R^{k} is the k𝑘k-dimensional word embedding and the semicolon is the concatenation operator. For the source matrix X1:Tsubscript𝑋:1𝑇X_{1:T}, a kernel wj∈Rl×ksubscript𝑤𝑗superscript𝑅𝑙𝑘{w_{j}}\in R^{l\times k} applies a convolutional operation to a window size of l𝑙l words to produce a series of feature maps:cj​i=ρ​(B​N​(wj⊗Xi:i+l−1+b))subscript𝑐𝑗𝑖𝜌𝐵𝑁tensor-productsubscript𝑤𝑗subscript𝑋:𝑖𝑖𝑙1𝑏c_{ji}=\rho(BN(w_{j}\otimes X_{i:i+l-1}+b))(3)where ⊗tensor-product\otimes operator is the summation of element-wise production and b𝑏b is a bias term. ρ𝜌\rho is a non-linear activation function which is implemented as ReLu in this paper. Note that the batch normalization Ioffe and Szegedy (2015) which accelerates the training significantly, is applied to the input of the activation function (B​N𝐵𝑁BN in equation 3). To get the final feature with respect to kernel wjsubscript𝑤𝑗w_{j}, a max-over-time pooling operation is leveraged over the feature maps:c~j=m​a​x​{cj​1,…,cj​T−l+1}subscript~𝑐𝑗𝑚𝑎𝑥subscript𝑐𝑗1…subscript𝑐𝑗𝑇𝑙1\widetilde{c}_{j}=max\{c_{j1},\ldots,c_{j{T-l+1}}\}(4)We use various numbers of kernels with different window sizes to extract different features, which are then concatenated to form the source-language sentence representation cxsubscript𝑐𝑥c_{x}. Identically, the target-language sentence representation cysubscript𝑐𝑦c_{y} can be extracted from the target matrix Y1:Tsubscript𝑌:1𝑇Y_{1:T}. Finally, given the source-language sentence, the probability that the target-language sentence is being real can be computed as:p=σ​(V​[cx;cy])𝑝𝜎𝑉subscript𝑐𝑥subscript𝑐𝑦p=\sigma(V[c_{x};c_{y}])(5)where V𝑉V is the transform matrix which transforms the concatenation of cxsubscript𝑐𝑥c_{x} and cysubscript𝑐𝑦c_{y} into a 2-dimension embedding and σ𝜎\sigma is the logistic function.

We apply the smoothed sentence-level BLEU as the specific objective for the generator. Given the generated sentence ygsubscript𝑦𝑔y_{g} and the the ground true sentence ydsubscript𝑦𝑑y_{d}, the objective Q𝑄Q calculates a reward Q​(yg,yd)𝑄subscript𝑦𝑔subscript𝑦𝑑Q(y_{g},y_{d}), which measures the n-gram precisions of the generated sentence ygsubscript𝑦𝑔y_{g}. Identical to the output of the discriminator, the Q​(yg,yd)𝑄subscript𝑦𝑔subscript𝑦𝑑Q(y_{g},y_{d}) also ranges from zero to one, which makes it easier to fuse Q𝑄Q and D𝐷D.

Following Yu et al. (2016), the objective of the generator G𝐺G is defined as to generate a sequence from the start state to maximize its expected end reward. Formally, the objective function is computed as:J​(θ)=∑Y1:TGθ​(Y1:T|X)⋅RD,QGθ​(Y1:T−1,X,yT,Y∗)𝐽𝜃subscriptsubscript𝑌:1𝑇⋅subscript𝐺𝜃conditionalsubscript𝑌:1𝑇𝑋superscriptsubscript𝑅𝐷𝑄subscript𝐺𝜃subscript𝑌:1𝑇1𝑋subscript𝑦𝑇superscript𝑌J(\theta)=\sum\limits_{Y_{1:T}}G_{\theta}(Y_{1:T}|X)\cdot R_{D,Q}^{G_{\theta}}(Y_{1:T-1},X,y_{T},Y^{*})where θ𝜃\theta represents the parameters in G𝐺G, Y1:T=y1,…,yTsubscript𝑌:1𝑇subscript𝑦1…subscript𝑦𝑇Y_{1:T}=y_{1},\ldots,y_{T} indicates the generated target sequence, X𝑋X is the source-language sentence, Y∗superscript𝑌Y^{*} represents the ground true target sentence.RD,QGθsuperscriptsubscript𝑅𝐷𝑄subscript𝐺𝜃R_{D,Q}^{G_{\theta}} is the action-value function of a target-language sentence given the source sentence X𝑋X, i.e. the expected accumulative reward starting from the state (Y1:T−1,X)subscript𝑌:1𝑇1𝑋(Y_{1:T-1},X), taking action yTsubscript𝑦𝑇y_{T}, and following the policy Gθsubscript𝐺𝜃G_{\theta}. To estimate the action-value function, we consider the estimated probability of being real by the discriminator D𝐷D and the output of the BLEU objective Q𝑄Q as the reward:RD,QGθ​(Y1:T−1,X,yT,Y∗)=λ​(D​(X,Y1:T)−b​(X,Y1:T))+(1−λ)​Q​(Y1:T,Y∗)missing-subexpressionsuperscriptsubscript𝑅𝐷𝑄subscript𝐺𝜃subscript𝑌:1𝑇1𝑋subscript𝑦𝑇superscript𝑌absentmissing-subexpression𝜆𝐷𝑋subscript𝑌:1𝑇𝑏𝑋subscript𝑌:1𝑇1𝜆𝑄subscript𝑌:1𝑇superscript𝑌\begin{aligned} &R_{D,Q}^{G_{\theta}}(Y_{1:T-1},X,y_{T},Y^{*})=\\&\lambda(D(X,Y_{1:T})-b(X,Y_{1:T}))+(1-\lambda)Q(Y_{1:T},Y^{*})\end{aligned}where b(X,Y) denotes the baseline value to reduce the variance of the reward. Practically, we take b(X,Y) as a constant, 0.5 for simplicity. And the λ𝜆\lambda is a hyper-parameter. The question is that, given the source sequence, D𝐷D only provides a reward value for a finished target sequence. If Y1:Tsubscript𝑌:1𝑇Y_{1:T} is not a finished target sequence, the value of D​(X,Y1:T)𝐷𝑋subscript𝑌:1𝑇D(X,Y_{1:T}) makes no sense. Therefore, we cannot get the action-value for an intermediate state directly. To evaluate the action-value for an intermediate state, the Monte Carlo search under the policy of Gθsubscript𝐺𝜃G_{\theta} is applied to sample the unknown tokens. Each search ends until the end of sentence token is sampled or the sampled sentence reaches the maximum length. To obtain more stable reward and reduce the variance, we represent an N-time Monte Carlo search as:{Y1:T11,…,Y1:TNN}=M​CGθ​((Y1:t,X),N)superscriptsubscript𝑌:1subscript𝑇11…superscriptsubscript𝑌:1subscript𝑇𝑁𝑁𝑀superscript𝐶subscript𝐺𝜃subscript𝑌:1𝑡𝑋𝑁\{Y_{1:T_{1}}^{1},\ldots,Y_{1:T_{N}}^{N}\}=MC^{G_{\theta}}((Y_{1:t},X),N)where Tisubscript𝑇𝑖T_{i} represents the length of the sentence sampled by the i𝑖i’th Monte Carlo search. (Y1:t,X)=(y1,…,yt,X)subscript𝑌:1𝑡𝑋subscript𝑦1…subscript𝑦𝑡𝑋(Y_{1:t},X)=(y_{1},\ldots,y_{t},X) is the current state and Yt+1:TNNsuperscriptsubscript𝑌:𝑡1subscript𝑇𝑁𝑁Y_{t+1:T_{N}}^{N} is sampled based on the policy Gθsubscript𝐺𝜃G_{\theta}. The discriminator provides N𝑁N rewards for the sampled N𝑁N sentences respectively. The final reward for the intermediate state is calculated as the average of the N𝑁N rewards. Hence, for the target sentence with the length T𝑇T, we compute the reward for ytsubscript𝑦𝑡y_{t} in the sentence level as:RD,QGθ​(Y1:t−1,X,yT,Y∗)={1N∑n=1Nλ(D(X,Y1:Tnn)−b(X,Y1:Tnn))+(1−λ)Q(Y1:Tn,Y∗)t<Tλ​(D​(X,Y1:t)−b​(X,Y1:t))+(1−λ)​Q​(Y1:t,Y∗)t=T\begin{aligned} &R_{D,Q}^{G_{\theta}}(Y_{1:t-1},X,y_{T},Y^{*})=\\&\left\{\begin{array}[]{lcl}\frac{1}{N}\sum\limits_{n=1}^{N}\lambda(D(X,Y_{1:T_{n}}^{n})-b(X,Y_{1:T_{n}}^{n}))+(1-\lambda)Q(Y_{1:T_{n}},Y*)&\text{$t<T$}\\\lambda(D(X,Y_{1:t})-b(X,Y_{1:t}))+(1-\lambda)Q(Y_{1:t},Y^{*})&\text{$t=T$}\end{array}\right.\end{aligned}Using the discriminator as a reward function can further improve the generator iteratively by dynamically updating the discriminator. Once we get more realistic generated sequences, we re-train the discriminator as:min−𝔼X,Y∈Pd​a​t​a​[log⁡D​(X,Y)]−𝔼X,Y∈G​[log⁡(1−D​(X,Y))]subscript𝔼𝑋𝑌subscript𝑃𝑑𝑎𝑡𝑎delimited-[]𝐷𝑋𝑌subscript𝔼𝑋𝑌𝐺delimited-[]1𝐷𝑋𝑌\min-\mathbb{E}_{X,Y\in P_{data}}[\log D(X,Y)]-\mathbb{E}_{X,Y\in G}[\log(1-D(X,Y))]After updating the discriminator, we are ready to re-train the generator. The gradient of the objective function J​(θ)𝐽𝜃J(\theta) w.r.t the generator’s parameter θ𝜃\theta is calculated as:∇J​(θ)=1T​∑t=1T∑ytRD,QGθ​(Y1:t−1,X,yT,Y∗)⋅∇θ(Gθ​(yt|Y1:t−1,X))=1T​∑t=1T𝔼yt∈Gθ​[RD,QGθ​(Y1:t−1,X,yT,Y∗)⋅∇θlog⁡p​(yt|Y1:t−1,X)]∇𝐽𝜃1𝑇superscriptsubscript𝑡1𝑇subscriptsubscript𝑦𝑡⋅superscriptsubscript𝑅𝐷𝑄subscript𝐺𝜃subscript𝑌:1𝑡1𝑋subscript𝑦𝑇superscript𝑌subscript∇𝜃subscript𝐺𝜃conditionalsubscript𝑦𝑡subscript𝑌:1𝑡1𝑋missing-subexpressionmissing-subexpressionabsent1𝑇superscriptsubscript𝑡1𝑇subscript𝔼subscript𝑦𝑡subscript𝐺𝜃delimited-[]⋅superscriptsubscript𝑅𝐷𝑄subscript𝐺𝜃subscript𝑌:1𝑡1𝑋subscript𝑦𝑇superscript𝑌subscript∇𝜃𝑝conditionalsubscript𝑦𝑡subscript𝑌:1𝑡1𝑋missing-subexpressionmissing-subexpression\begin{array}[]{lcl}\nabla J(\theta)=\frac{1}{T}\sum\limits_{t=1}^{T}\sum\limits_{y_{t}}R_{D,Q}^{G_{\theta}}(Y_{1:t-1},X,y_{T},Y^{*})\cdot\nabla_{\theta}(G_{\theta}(y_{t}|Y_{1:t-1},X))&\\=\frac{1}{T}\sum\limits_{t=1}^{T}\mathbb{E}_{y_{t}\in G_{\theta}}[R_{D,Q}^{G_{\theta}}(Y_{1:t-1},X,y_{T},Y^{*})\cdot\nabla_{\theta}\log p(y_{t}|Y_{1:t-1},X)]\end{array}

GANs are widely criticized for its unstable training since the generator and discriminator need to be carefully synchronized. To make this work easier to reproduce, this paper gives detailed strategies for training the proposed model.

Firstly, we use the maximum likelihood estimation to pre-train the generator on the parallel training set until the best translation performance is achieved. Then, generate the machine-generated sentences by using the generator to decode the training data. We simply use the greedy sampling method instead of the beam search method for decoding. Next, pre-train the discriminator on the combination of the true parallel data and the machine-generated data until the classification accuracy achieves at ξ𝜉\xi. Finally, we jointly train the generator and discriminator. The generator is trained with the policy gradient training method. However, in our practice, we find that updating the generator only with the simple policy gradient training leads to unstableness. To alleviate this issue, we adopt the teacher forcing approach which is similar to Lamb et al. (2016); Li et al. (2017). We directly make the discriminator to automatically assign a reward of 1 to the golden target-language sentence and the generator uses this reward to update itself on the true parallel example. We run the teacher forcing training for one time once the generator is updated by the policy gradient training. After the generator gets updated, we use the new stronger generator to generate η𝜂\eta more realistic sentences, which are then used to train the discriminator. Following Arjovsky et al. (2017), we clamp the weights of the discriminator to a fixed box ( [−ϵitalic-ϵ-\epsilon,ϵitalic-ϵ\epsilon] ) after each gradient update. We perform one optimization step for the discriminator for each step of the generator. In our practice, we set ξ𝜉\xi as 0.82, η𝜂\eta as 5000, ϵitalic-ϵ\epsilon as 1.0 and the N𝑁N for Monte Carlo search as 20.

We evaluate our BR-CSGAN on English-German and Chinese-English translation tasks and we test two different architectures for the generator, the traditional RNNSearch and the newly emerged state-of-the-art Transformer.

English-German: For English-German translation, we conduct our experiments on the publicly available corpora used extensively as benchmark for NMT systems, WMT’14 En-De. This data set contains 4.5M sentence pairs 444http://nlp.stanford.edu/projects/nmt. Sentences are encoded using byte-pair encoding Sennrich et al. (2015), which has a shared source-target vocabulary of about 37000 tokens.We report results on newstest2014. The newstest2013 is used as validation.

Chinese-English: For Chinese-English translation, our training data consists of 1.6M sentence pairs randomly extracted from LDC corpora 555LDC2002L27, LDC2002T01, LDC2002E18, LDC2003E07, LDC2004T08, LDC2004E12, LDC2005T10. Both the source and target sentences are encoded with byte-pair encoding and the tokens in the source and target vocabulary is about 38000 and 34000 respectively 666When doing BPE for Chinese, we need to do word segmentation first and the following steps are the same with BPE for English.. We choose the NIST02 as the development set. For testing, we use NIST03, NIST04 and NIST05 data sets.

To speed up the training procedure, sentences of length over 50 words are removed when we conduct experiments on the RNNSearch model. This is widely used by previous works Ranzato et al. (2015); Shen et al. (2015); Yang et al. (2016).

For the Transformer, following the base model in Vaswani et al. (2017), we set the dimension of word embedding as 512, dropout rate as 0.1 and the head number as 8. The encoder and decoder both have a stack of 6 layers. We use beam search with a beam size of 4 and length penalty α=0.6𝛼0.6\alpha=0.6. For the RNNSearch, following Bahdanau et al. (2014), We set the hidden units for both encoders and decoders as 512. The dimension of the word embedding is also set as 512. We do not apply dropout for training the RNNSearch. During testing, we use beam search with a beam size of 10 and length penalty is not applied.

All models are implemented in TensorFlow Abadi et al. (2015) and trained on up to four K80 GPUs synchronously in a multi-GPU setup on a single machine 777The code we used to train and evaluate our models can be found at https://github.com/ZhenYangIACAS/NMT_GAN. We stop training when the model achieves no improvement for the tenth evaluation on the development set. BLEU Papineni et al. (2002) is utilized as the evaluation metric. We apply the script mteval-v11b.pl to evaluate the Chinese-English translation and utilize the script multi-belu.pl for English-German translation 888https://github.com/moses-smt/mosesdecoder/blob/617e8c8/scripts/generic/multi-bleu.perl;mteval-v11b.pl.

The model of RNNSearch is optimized with the mini-batch of 64 examples. It takes about 30 hours to pre-train the RNNSearch on the Chinese-English data set and 46 hours on the English-German data set. During generative adversarial training, it takes about 35 hours on the Chinese-English data set and about 50 hours on the English-German data set. For the Transformer, each training batch contains a set of sentence pairs containing approximately 25000 source tokens and 25000 target tokens. On the Chinese-English data set, it takes about 15 hours to do pre-training and 20 hours to do generative adversarial training. On the English-German data set, it takes about 35 hours for the pre-training and 40 hours for the generative adversarial training.

Table 1 shows the BLEU score on Chinese-English and English-German test sets. On the RNNSearch model, the naive GAN (i.e., the line of RNNSearch+BR-CSGAN (λ𝜆\lambda=1) in table 1) achieves improvement up to +1.11 BLEU points averagely on Chinese-English test sets and +0.9 BLEU points on English-German test set. Armed with the BLEU objective, the BR-CSGAN (the line of RNNSearch+BR-CSGAN (λ𝜆\lambda=0.7)) leads to more significant improvements, +1.83 BLEU points averagely on Chinese-English translation and +1.69 BLEU points on English-German translation. We also test the translation performance when the RNNSearch is only guided by the static BLEU objective (the line of RNNSearch+BR-CSGAN (λ𝜆\lambda=0)), and we only get +0.58 BLEU points improvement on Chinese-English translation and +0.55 BLEU points improvement on English-German. Experiments on the Transformer show the same trends. While the Transformer has achieved state-of-the-art translation performances, our approach still achieves +0.81 BLEU points improvement on Chinese-English translation and +0.62 BLEU points improvement on English-German.

These results indicate that the proposed BR-CSGAN consistently outperforms the baselines and it shows better translation performance than the naive GAN and the model guided only by the BLEU objective.

We show that MRT Shen et al. (2015) is an extreme case of our approach. Considering a sentence pair (x,y)𝑥𝑦(x,y), the training objective of MRT is calculated asJ^​(θ′)=∑ys∈S​(x)p​(ys|x;θ′)​Δ​(ys,y)^𝐽superscript𝜃′subscriptsuperscript𝑦𝑠𝑆𝑥𝑝conditionalsuperscript𝑦𝑠𝑥superscript𝜃′Δsuperscript𝑦𝑠𝑦\widehat{J}(\theta^{\prime})=\sum\limits_{y^{s}\in S(x)}p(y^{s}|x;\theta^{\prime})\Delta(y^{s},y)where Δ​(ys,y)Δsuperscript𝑦𝑠𝑦\Delta(y^{s},y) is a loss function (i.e., the sentence-level BLEU used in this paper) that measures the discrepancy between a predicted translation yssuperscript𝑦𝑠y^{s} and the training example y𝑦y, S​(x)𝑆𝑥S(x) represents the set which contains all of the predictions given the input x𝑥x, and θ′superscript𝜃′\theta^{\prime} is the parameters of the NMT model. Unfortunately, this objective is usually intractable due to the exponential search space. To alleviate this problem, a subset of the search space is sampled to approximate this objective. In this paper, when we set λ𝜆\lambda as zero, the objective for the proposed BR-CSGAN comes toJ​(θ)λ=0=∑Y1:TGθ​(Y1:T|X)⋅Q​(Y1:T,Y∗)𝐽subscript𝜃𝜆0subscriptsubscript𝑌:1𝑇⋅subscript𝐺𝜃conditionalsubscript𝑌:1𝑇𝑋𝑄subscript𝑌:1𝑇superscript𝑌J(\theta)_{\lambda=0}=\sum\limits_{Y_{1:T}}G_{\theta}(Y_{1:T}|X)\cdot Q(Y_{1:T},Y^{*})where the Q​(Y1:T,Y∗)𝑄subscript𝑌:1𝑇superscript𝑌Q(Y_{1:T},Y^{*}) is also a loss function between the predicted translation Y1:Tsubscript𝑌:1𝑇Y_{1:T} and the training example Y∗superscript𝑌Y^{*}. It is easy to be found that, under this condition (i.e., λ𝜆\lambda set as zero), the proposed BR-CSGAN optimizes almost the same objective with MRT. The only difference is that the reinforcement learning procedure is utilized in BR-CSGAN to maximize the total reward and MRT instead applies random sampling to approximate the risk. Actually, the BR-CSGAN is a weighted sum of the naive GAN (λ𝜆\lambda=1) and MRT (λ𝜆\lambda=0), and it incorporates the advantages of the two approaches. Specifically, compared to naive GAN which is trained without specific objective guidance, BR-CSGAN utilizes the BLEU objective to guide the generator to generate sentences with higher BLEU points. And compared to MRT which is trained only with the static objective, the BR-CSGAN applies a dynamic discriminator which updates synchronously with the generator, to feedback the dynamic rewards for the generator. Table 2 compares the translation performance between the MRT and BR-CSGAN on Chinese-English and English-German translation tasks. We only conduct experiments on the RNNSearch because we only get the open-source implementation of MRT on the RNNSearch 999The open-source implementation can be found at: https://github.com/EdinburghNLP/nematus. Results show that the proposed BR-CSGAN consistently outperforms the MRT on the Chinese-English and English-German translations.

The initial accuracy ξ𝜉\xi of the discriminator which is viewed as a hyper-parameter, can be set carefully during the process of pre-training. A natural question is that when shall we end the pre-training. Do we need to pre-train the discriminator with the highest accuracy? To answer this question, we test the impact of the initial accuracy of the discriminator. We pre-train five discriminators which have the accuracy as 0.6, 0.7, 0.8, 0.9 and 0.95 respectively. With the five discriminators, we train five different BR-CSGAN models (with the generator as RNNSearch and λ𝜆\lambda set as 0.7) and test their translation performances on the development set at regular intervals. Figure 2 reports the results and we can find that the initial accuracy of the discriminator shows great impacts on the translation performance of the proposed BR-CSGAN. From figure 2, we show that the initial accuracy of the discriminator needs to be set carefully and either it is too high (0.9 and 0.95) or too low (0.6 and 0.7), the model performs badly 101010To make the illustration simple and clear, we only depict the results when the RNNSearch acts as the generator.. This suggests that it is important for the generator and discriminator to keep a balanced relationship at the beginning of the generative adversarial training. If the discriminator is too strong, the generator is always penalized for its bad predictions and gets no idea about right predictions. Hence, the generator is discouraged all the time and the performance gets worse and worse. On the other hand, if the discriminator is too weak, the discriminator is unable to give right guidance for the generator, i.e. the gradient direction for updating the generator is random. Empirically, we pre-train the discriminator until its accuracy reaches around 0.8.

We are also curious about how the sample times N𝑁N for Monte Carlo search affects the translation performance. Intuitively, if N𝑁N is set as a small number, the intermediate reward for each word may be incorrect since there is a large variance for the Monto Carol search when the sample time is too small. And if otherwise, the computation shall be very time consuming because we need to do much more sampling. Therefore, there is a trade-off between the accuracy and computation complexity here. We investigate this problem on the Chinese-English translation task. Table 3 presents the translation performance of the BR-CSGAN on the test sets when the N𝑁N are set from 5 to 30 with interval 5. From table 3, the proposed model achieves no improvement than the baseline (i.e., the pre-trained generator) when N𝑁N are set less than 15 and the BLEU scores are not reported on the table. As a matter of fact, the translation performance of the model gets worse and worse. We conjecture that the approximated reward is far from the expected reward due to the large variance when N𝑁N is set too small, and gives wrong gradient directions for model updating. Since the training for GAN is not stable, the wrong gradient direction exacerbates the unstableness and results in the BLEU getting worse and worse. With the increasing of N𝑁N, the translation performance of the model gets improved. However, with N𝑁N set larger than 20, we get little improvement than the model with N𝑁N set as 20 and the training time exceeds our expectation.

In this work, we propose the BR-CSGAN which leverages the BLEU reinforced generative adversarial net to improve the NMT. We show that the proposed approach is a weighted combination of the naive GAN and MRT. To verify the effectiveness of our approach, we test two different architectures for the generator, the traditional RNNSearch and the state-of-the-art Transformer. Extensive experiments on Chinese-English and English-German translation tasks show that our approach consistently achieves significant improvements. In the future, we would like to try multi-adversarial framework which consists of multi discriminators and generators for GAN.