Introduction
Natural text generation, as a key task in NLP, has been advanced substantially thanks to the flourish of neural models BIBREF0 , BIBREF1 . Typical frameworks such as sequence-to-sequence (seq2seq) have been applied to various generation tasks, including machine translation BIBREF2 and dialogue generation BIBREF3 . The standard paradigm to train such neural models is maximum likelihood estimation (MLE), which maximizes the log-likelihood of observing each word in the text given the ground-truth proceeding context BIBREF4 .
Although widely used, MLE suffers from the exposure bias problem BIBREF5 , BIBREF6 : during test, the model sequentially predicts the next word conditioned on its previous generated words while during training conditioned on ground-truth words. To tackle this problem, generative adversarial networks (GAN) with reinforcement learning (RL) training approaches have been introduced to text generation tasks BIBREF7 , BIBREF8 , BIBREF9 , BIBREF10 , BIBREF11 , BIBREF12 , BIBREF13 , where the discriminator is trained to distinguish real and generated text samples to provide reward signals for the generator, and the generator is optimized via policy gradient BIBREF7 .
However, recent studies have shown that potential issues of training GANs on discrete data are more severe than exposure bias BIBREF14 , BIBREF15 . One of the fundamental issues when generating discrete text samples with GANs is training instability. Updating the generator with policy gradient always leads to an unstable training process because it's difficult for the generator to derive positive and stable reward signals from the discriminator even with careful pre-training BIBREF8 . As a result, the generator gets lost due to the high variance of reward signals and the training process may finally collapse BIBREF16 .
In this paper, we propose a novel adversarial training framework called Adversarial Reward Augmented Maximum Likelihood (ARAML) to deal with the instability issue of training GANs for text generation. At each iteration of adversarial training, we first train the discriminator to assign higher rewards to real data than to generated samples. Then, inspired by reward augmented maximum likelihood (RAML) BIBREF17 , the generator is updated on the samples acquired from a stationary distribution with maximum likelihood estimation (MLE), weighted by the discriminator's rewards. This stationary distribution is designed to guarantee that training samples are surrounding the real data, thus the exploration space of our generator is indeed restricted by the MLE training objective, resulting in more stable training. Compared to other text GANs with RL training techniques, our framework acquires samples from the stationary distribution rather than the generator's distribution, and uses RAML training paradigm to optimize the generator instead of policy gradient. Our contributions are mainly as follows:
Related Work
Recently, text generation has been widely studied with neural models trained with maximum likelihood estimation BIBREF4 . However, MLE tends to generate universal text BIBREF18 . Various methods have been proposed to enhance the generation quality by refining the objective function BIBREF18 , BIBREF19 or modifying the generation distribution with external information like topic BIBREF20 , sentence type BIBREF21 , emotion BIBREF22 and knowledge BIBREF23 .
As mentioned above, MLE suffers from the exposure bias problem BIBREF5 , BIBREF6 . Thus, reinforcement learning has been introduced to text generation tasks such as policy gradient BIBREF6 and actor-critic BIBREF24 . BIBREF17 proposed an efficient and stable approach called Reward Augmented Maximum Likelihood (RAML), which connects the log-likelihood and expected rewards to incorporate MLE training objective into RL framework.
Since some text generation tasks have no explicit metrics to be directly optimized, adversarial training has been applied to generating discrete text samples with a discriminator to learn a proper reward. For instance, SeqGAN BIBREF7 devised a discriminator to distinguish the real data and generated samples, and a generator to maximize the reward from the discriminator via policy gradient. Other variants of GANs have been proposed to improve the generator or the discriminator. To improve the generator, MaliGAN BIBREF8 developed a normalized maximum likelihood optimization target for the generator to stably model the discrete sequences. LeakGAN BIBREF11 guided the generator with reward signals leaked from the discriminator at all generation steps to deal with long text generation task. MaskGAN BIBREF10 employed an actor-critic architecture to make the generator fill in missing text conditioned on the surrounding context, which is expected to mitigate the problem of mode collapse. As for the discriminator, RankGAN BIBREF9 replaced traditional discriminator with a ranker to learn the relative ranking information between the real texts and generated ones. Inverse reinforcement learning BIBREF12 used a trainable reward approximator as the discriminator to provide dense reward signals at each generation step. DPGAN BIBREF13 introduced a language model based discriminator and regarded cross-entropy as rewards to promote the diversity of generation results.
The most similar works to our model are RAML BIBREF17 and MaliGAN BIBREF8 : 1) Compared with RAML, our model adds a discriminator to learn the reward signals instead of choosing existing metrics as rewards. We believe that our model can adapt to various text generation tasks, particularly those without explicit evaluation metrics. 2) Unlike MaliGAN, we acquire samples from a fixed distribution near the real data rather than the generator's distribution, which is expected to make the training process more stable.
Task Definition and Model Overview
Text generation can be formulated as follows: given the real data distribution INLINEFORM0 , the task is to train a generative model INLINEFORM1 where INLINEFORM2 can fit INLINEFORM3 well. In this formulation, INLINEFORM4 and INLINEFORM5 denotes a word in the vocabulary INLINEFORM6 .
Figure FIGREF3 shows the overview of our model ARAML. This adversarial training framework consists of two phases: 1) The discriminator is trained to assign higher rewards to real data than to generated data. 2) The generator is trained on the samples acquired from a stationary distribution with reward augmented MLE training objective. This training paradigm of the generator indeed constrains the search space with the MLE training objective, which alleviates the issue of unstable training.
Discriminator
The discriminator INLINEFORM0 aims to distinguish real data and generated data like other GANs. Inspired by Least-Square GAN BIBREF25 , we devise the loss function as follows: DISPLAYFORM0
This loss function forces the discriminator to assign higher rewards to real data than to generated data, so the discriminator can learn to provide more proper rewards as the training proceeds.
Generator
The training objective of our generator INLINEFORM0 is derived from the objective of other discrete GANs with RL training method: DISPLAYFORM0
where INLINEFORM0 denotes the rewards from the discriminator INLINEFORM1 and the entropy regularized term INLINEFORM2 encourages INLINEFORM3 to generate diverse text samples. INLINEFORM4 is a temperature hyper-parameter to balance these two terms.
As mentioned above, discrete GANs suffer from the instability issue due to policy gradient, thus they are consequently difficult to train. Inspired by RAML BIBREF17 , we introduce an exponential payoff distribution INLINEFORM0 to connect RL loss with RAML loss: DISPLAYFORM0
where INLINEFORM0 . Thus, we can rewrite INLINEFORM1 with INLINEFORM2 and INLINEFORM3 as follows: DISPLAYFORM0
Following RAML, we remove the constant term and optimize the KL divergence in the opposite direction: DISPLAYFORM0
where INLINEFORM0 is a constant in the training phase of the generator. It has been proved that INLINEFORM1 and INLINEFORM2 are equivalent up to their first order Taylor approximations, and they have the same global optimum BIBREF17 . INLINEFORM3 can be trained in a MLE-like fashion but sampling from the distribution INLINEFORM4 is intractable in the adversarial setting, because INLINEFORM5 varies with the discriminator INLINEFORM6 . Thus, we introduce importance sampling to separate sampling process from INLINEFORM7 and obtain the final loss function: DISPLAYFORM0
where INLINEFORM0 denotes a stationary distribution and INLINEFORM1 . To optimize this loss function, we first construct the fixed distribution INLINEFORM2 to get samples, and devise the proper reward function INLINEFORM3 to train the generator in a stable and effective way.
We construct the distribution INLINEFORM0 based on INLINEFORM1 : DISPLAYFORM0
In this way, INLINEFORM0 can be designed to guarantee that INLINEFORM1 is near INLINEFORM2 , leading to a more stable training process. To obtain a new sample INLINEFORM3 from a real data sample INLINEFORM4 , we can design three steps which contain sampling an edit distance INLINEFORM5 , the positions INLINEFORM6 for substitution and the new words INLINEFORM7 filled into the corresponding positions. Thus, INLINEFORM8 can be decomposed into three terms: DISPLAYFORM0
The first step is to sample an edit distance based on a real data sample INLINEFORM0 , where INLINEFORM1 is a sequence of length INLINEFORM2 . The number of sentences which have the edit distance INLINEFORM3 to some input sentence can be computed approximately as below: DISPLAYFORM0
where INLINEFORM0 denotes the number of sentences which have an edit distance INLINEFORM1 to a sentence of length INLINEFORM2 , and INLINEFORM3 indicates the size of vocabulary. We then follow BIBREF17 to re-scale the counts by INLINEFORM4 and do normalization, so that we can sample an edit distance INLINEFORM5 from: DISPLAYFORM0
where INLINEFORM0 , as a temperature hyper-parameter, restricts the search space surrounding the original sentence. Larger INLINEFORM1 brings more samples with long edit distances.
The next step is to select positions for substitution based on the sampled edit distance INLINEFORM0 . Intuitively, we can randomly choose INLINEFORM1 distinct positions in INLINEFORM2 to be replaced by new words. The probability of choosing the position INLINEFORM3 is calculated as follows: DISPLAYFORM0
Following this sampling strategy, we can obtain the position set INLINEFORM0 . This strategy approximately guarantees that the edit distance between a new sentence and the original sentence is INLINEFORM1 .
At the final step, our model determines new words for substitution at each sampled position INLINEFORM0 . We can formulate this sampling process from the original sequence INLINEFORM1 to a new sample INLINEFORM2 as a sequential transition INLINEFORM3 . At each step from INLINEFORM4 to INLINEFORM5 INLINEFORM6 , we first sample a new word INLINEFORM7 from the distribution INLINEFORM8 , then replace the old word at position INLINEFORM9 of INLINEFORM10 to obtain INLINEFORM11 . The whole sampling process can be decomposed as follows: DISPLAYFORM0
There are two common sampling strategies to model INLINEFORM0 , i.e. random sampling and constrained sampling. Random sampling strategy samples a new word INLINEFORM1 according to the uniform distribution over the vocabulary INLINEFORM2 BIBREF17 , while constrained sampling strategy samples INLINEFORM3 to maximize the language model score of the target sentence INLINEFORM4 BIBREF26 , BIBREF27 . Here, we adopt constrained sampling in our model and compare the performances of two strategies in the experiment.
We devise the reward function INLINEFORM0 according to the discriminator's output INLINEFORM1 and the stationary distribution INLINEFORM2 : DISPLAYFORM0
Intuitively, this reward function encourages the generator to generate sentences with large sampling probability and high rewards from the discriminator. Thus, the weight of samples INLINEFORM0 can be calculated as follows: DISPLAYFORM0
So far, we can successfully optimize the generator's loss INLINEFORM0 via Equation EQREF12 . This training paradigm makes our generator avoid possible variances caused by policy gradient and get more stable reward signals from the discriminator, because our generator is restricted to explore the training samples near the real data.
[htb] Adversarial Reward Augmented Maximum Likelihood [1]
Total adversarial training iterations: INLINEFORM0
Steps of training generator: INLINEFORM0
Steps of training discriminator: INLINEFORM0
Pre-train the generator INLINEFORM0 with MLE loss Generate samples from INLINEFORM1 Pre-train the discriminator INLINEFORM2 via Eq.( EQREF6 ) Construct INLINEFORM3 via Eq.( EQREF14 ) - Eq.( EQREF19 ) each INLINEFORM4 each INLINEFORM5 Update INLINEFORM6 via Eq.( EQREF12 ) each INLINEFORM7 Update INLINEFORM8 via Eq.( EQREF6 )
Extension to Conditional Text Generation
We have shown our adversarial training framework for text generation tasks without an input. Actually, it can also be extended to conditional text generation tasks like dialogue generation. Given the data distribution INLINEFORM0 where INLINEFORM1 denote contexts and responses respectively, the objective function of ARAML's generator can be modified as below: DISPLAYFORM0
where INLINEFORM0 and INLINEFORM1 is trained to distinguish whether INLINEFORM2 is the true response to INLINEFORM3 .
Comparison with RAML and MaliGAN
The most similar works to our framework are RAML BIBREF17 and MaliGAN BIBREF8 . The main difference among them is the training objective of their generators. We have shown different objective functions in Table TABREF26 . For comparison, we use the form with no input for all the three models.
Our model is greatly inspired by RAML, which gets samples from a non-parametric distribution INLINEFORM0 constructed based on a specific reward. Compared to RAML, our reward comes from a learnable discriminator which varies as the adversarial training proceeds rather than a specific reward function. This difference equips our framework with the ability to adapt to the text generation tasks with no explicit evaluation metrics as rewards.
Our model is also similar to MaliGAN, which gets samples from the generator's distribution. In MaliGAN's training objective, INLINEFORM0 also indicates the generator's distribution but it's used in the sampling phase and fixed at each optimization step. The weight of samples INLINEFORM1 . Different from our model, MaliGAN acquires samples from the generator's distribution INLINEFORM2 , which usually brings samples with low rewards even with careful pre-training for the generator, leading to training instability. Instead, our framework gets samples from a stationary distribution INLINEFORM3 around real data, thus our training process is more stable.
Datasets
We evaluated ARAML on three datasets: COCO image caption dataset BIBREF28 , EMNLP2017 WMT dataset and WeiboDial single-turn dialogue dataset BIBREF29 . COCO and EMNLP2017 WMT are the common benchmarks with no input to evaluate the performance of discrete GANs, and we followed the existing works to preprocess these datasets BIBREF12 , BIBREF11 . WeiboDial, as a dialogue dataset, was applied to test the performance of our model with input trigger. We simply removed post-response pairs containing low-frequency words and randomly selected a subset for our training/test set. The statistics of three datasets are presented in Table TABREF28 .
Baselines
We compared our model with MLE, RL and GAN baselines. Since COCO and EMNLP2017 WMT don't have input while WeiboDial regards posts as input, we chose the following baselines respectively:
MLE: a RNN model trained with MLE objective BIBREF4 . Its extension, Seq2Seq, can work on the dialogue dataset BIBREF2 .
SeqGAN: The first text GAN model that updates the generator with policy gradient based on the rewards from the discriminator BIBREF7 .
LeakGAN: A variant of SeqGAN that provides rewards based on the leaked information of the discriminator for the generator BIBREF11 .
MaliGAN: A variant of SeqGAN that optimizes the generator with a normalized maximum likelihood objective BIBREF8 .
IRL: This inverse reinforcement learning method replaces the discriminator with a reward approximator to provide dense rewards BIBREF12 .
RAML: A RL approach to incorporate MLE objective into RL training framework, which regards BLEU as rewards BIBREF17 .
DialogGAN: An extension of SeqGAN tuned to dialogue generation task with MLE objective added to the adversarial objective BIBREF16 .
DPGAN: A variant of DialogGAN which uses a language model based discriminator and regards cross-entropy as rewards BIBREF13 .
Note that MLE, SeqGAN, LeakGAN, MaliGAN and IRL are the baselines on COCO and EMNLP2017 WMT, while MLE, RAML, DialogGAN, and DPGAN on WeiboDial. The original codes are used to test the baselines.
Implementation Details
The implementation details of our model are shown in Table TABREF31 . For COCO / EMNLP2017, the generator is a LSTM unit BIBREF30 with 128 cells, and the discriminator is implemented based on BIBREF7 . For WeiboDial, the generator is an encoder-decoder structure with attention mechanism, where both the encoder and the decoder consist of a two-layer GRU BIBREF31 with 128 cells. The discriminator is implemented based on BIBREF32 . The language model used in the constrained sampling of ARAML is implemented in the same setting as the generators, and is pre-trained on the training set of each dataset. The codes and the datasets are available at https://github.com/kepei1106/ARAML.
As for the details of the baselines, the generators of all the baselines except LeakGAN are the same as ours. Note that the generator of LeakGAN consists of a hierarchical LSTM unit, thus we followed the implementation in the original paper. In terms of the differences, the discriminators of GAN baselines are implemented based on the original papers. Other hyper-parameters of baselines including batch size, learning rate, and pre-training epochs, were set based on the original codes, because the convergence of baselines is sensitive to these hyper-parameters.
Language Generation on COCO and EMNLP2017 WMT
We adopted forward/reverse perplexity BIBREF33 and Self-BLEU BIBREF34 to evaluate the quality of generated texts. Forward perplexity (PPL-F) indicates the perplexity on the generated data provided by a language model trained on real data to measure the fluency of generated samples. Reverse perplexity (PPL-R) switches the roles of generated data and real data to reflect the discrepancy between the generated distribution and the data distribution. Self-BLEU (S-BLEU) regards each sentence in the generated collection as hypothesis and the others as reference to obtain BLEU scores, which evaluates the diversity of generated results.
Results are shown in Table TABREF33 . LeakGAN performs best on forward perplexity because it can generate more fluent samples. As for reverse perplexity, our model ARAML beats other baselines, showing that our model can fit the data distribution better. Other GANs, particularly LeakGAN, obtain high reverse perplexity due to mode collapse BIBREF12 , thus they only capture limited fluent expressions, resulting in large discrepancy between the generated distribution and data distribution. ARAML also outperforms the baselines in terms of Self-BLEU, indicating that our model doesn't fall into mode collapse with the help of the MLE training objective and has the ability to generate more diverse sentences.
We also provide standard deviation of each metric in Table TABREF33 , reflecting the stability of each model's performance. Our model ARAML nearly achieves the smallest standard deviation in all the metrics, indicating that our framework outperforms policy gradient in the stability of adversarial training.
Dialogue Generation on WeiboDial
Dialogue evaluation is an open problem and existing works have found that automatic metrics have low correlation to human evaluation BIBREF35 , BIBREF36 , BIBREF37 . Thus, we resorted to manual evaluation to assess the generation quality on WeiboDial. We randomly sampled 200 posts from the test set and collected the generated results from all the models. For each pair of responses (one from ARAML and the other from a baseline, given the same input post), five annotators were hired to label which response is better (i.e. win, lose or tie) in terms of grammaticality (whether a response itself is grammatical and logical) and relevance (whether a response is appropriate and relevant to the post). The two metrics were evaluated independently.
The evaluation results are shown in Table TABREF35 . To measure the inter-annotator agreement, we calculated Fleiss' kappa BIBREF38 for each pair-wise comparison where results show moderate agreement ( INLINEFORM0 ). We also conducted sign test to check the significance of the differences.
As shown in Table TABREF35 , ARAML performs significantly better than other baselines in all the cases. This result indicates that the samples surrounding true responses provide stable rewards for the generator, and stable RAML training paradigm significantly enhances the performance in both metrics.
Further Analysis on Stability
To verify the training stability, we conducted experiments on COCO many times and chose the best 5 trials for SeqGAN, LeakGAN, IRL, MaliGAN and ARAML, respectively. Then, we presented the forward/reverse perplexity in the training process in Figure FIGREF38 . We can see that our model with smaller standard deviation is more stable than other GAN baselines in both metrics. Although LeakGAN reaches the best forward perplexity, its standard deviation is extremely large and it performs badly in reverse perplexity, indicating that it generates limited expressions that are grammatical yet divergent from the data distribution.
Ablation Study
The temperature INLINEFORM0 controls the search space surrounding the real data as we analyze in Section UID13 . To investigate its impact on the performance of our model, we fixed all the other hyper-parameters and test ARAML with different temperatures on COCO.
The experimental results are shown in Figure FIGREF41 . We can see that as the temperature becomes larger, forward perplexity increases gradually while Self-BLEU decreases. As mentioned in Section UID13 , large temperatures encourage our generator to explore the samples that are distant from real data distribution, thus the diversity of generated results will be improved. However, these samples distant from the data distribution are more likely to be poor in fluency, leading to worse forward perplexity. Reverse perplexity is influenced by both generation quality and diversity, so the correlation between temperature and reverse perplexity is not intuitive. We can observe that the model with INLINEFORM0 reaches the best reverse perplexity.
We have mentioned two common sampling strategies in Section UID13 , i.e. random sampling and constrained sampling. To analyze their impact, we keep all the model structures and hyper-parameters fixed and test ARAML with these two strategies on COCO.
Table TABREF45 shows the results. It's obvious that random sampling hurts the model performance except Self-BLEU-1, because it indeed allows low-quality samples available to the generator. Exploring these samples degrades the quality and diversity of generated results. Despite the worse performance on automatic metrics, random sampling doesn't affect the training stability of our framework. The standard deviation of ARAML-R is still smaller than other GAN baselines.
Case Study
Table TABREF47 presents the examples generated by the models on COCO. We can find that other baselines suffer from grammatical errors (e.g. “in front of flying her kite" from MLE), repetitive expressions (e.g. “A group of people" from IRL) and incoherent statements (e.g. “A group of people sitting on a cell phone” from IRL). By contrast, our model performs well in these sentences and has the ability to generate grammatical and coherent results.
Table TABREF48 shows the generated examples on WeiboDial. It's obvious that other baselines don't capture the topic word “late" in the post, thus generate irrelevant responses. ARAML can provide a response that is grammatical and closely relevant to the post.
Conclusion
We propose a novel adversarial training framework to deal with the instability problem of current GANs for text generation. To address the instability issue caused by policy gradient, we incorporate RAML into the advesarial training paradigm to make our generator acquire stable rewards. Experiments show that our model performs better than several state-of-the-art GAN baselines with lower training variance, yet producing better performance on three text generation tasks.
Acknowledgments
This work was supported by the National Science Foundation of China (Grant No. 61936010/61876096) and the National Key R&D Program of China (Grant No. 2018YFC0830200). We would like to thank THUNUS NExT Joint-Lab for the support.

Question: What GAN models were used as baselines to compare against?
Answer: MLE, SeqGAN, LeakGAN, MaliGAN, IRL, RAML, DialogGAN, DPGAN

SeqGAN, LeakGAN, MaliGAN, DialogGAN, DPGAN

Question: How much improvement is gained from Adversarial Reward Augmented Maximum Likelihood (ARAML)?
Answer: ARAM has achieved improvement over all baseline methods using reverese perplexity and  slef-BLEU metric.  The maximum reverse perplexity improvement 936,16 is gained for EMNLP2017  WMT  dataset and  48,44 for COCO dataset.

Compared to the baselines, ARAML does not do better in terms of perplexity on COCO and EMNLP 2017 WMT datasets, but it does by up to 0.27 Self-BLEU points on COCO and 0.35 Self-BLEU on EMNLP 2017 WMT. In terms of Grammaticality and Relevance, it scores better than the baselines on up to 75.5% and 73% of the cases respectively.

Question: Is the discriminator's reward made available at each step to the generator?
Answer: Unanswerable