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Title: Connecting the Dots Between MLE and RL for Sequence Generation

Paper content:
Sequence generation models such as recurrent networks can be trained with a diverse set of learning algorithms.
For example, maximum likelihood learning is simple and efficient, yet suffers from the exposure bias problem.
Reinforcement learning like policy gradient addresses the problem but can have prohibitively poor exploration efficiency.
A variety of other algorithms such as RAML, SPG, and data noising, have also been developed in different perspectives.
This paper establishes a formal connection between these algorithms.
We present a generalized entropy regularized policy optimization formulation, and show that the apparently divergent algorithms can all be reformulated as special instances of the framework, with the only difference being the configurations of reward function and a couple of hyperparameters.
The unified interpretation offers a systematic view of the varying properties of exploration and learning efficiency.
Besides, based on the framework, we present a new algorithm that dynamically interpolates among the existing algorithms for improved learning.
Experiments on machine translation and text summarization demonstrate the superiority of the proposed algorithm.
Sequence generation is a ubiquitous problem in many applications, such as machine translation BID28 , text summarization BID13 BID25 , image captioning BID15 , and so forth.
Great advances in these tasks have been made by the development of sequence models such as recurrent neural networks (RNNs) with different cells BID12 BID6 and attention mechanisms BID1 BID19 .
These models can be trained with a variety of learning algorithms.The standard training algorithm is based on maximum-likelihood estimation (MLE) which seeks to maximize the log-likelihood of ground-truth sequences.
Despite the computational simplicity and efficiency, MLE training suffers from the exposure bias BID24 .
That is, the model is trained to predict the next token given the previous ground-truth tokens; while at test time, since the resulting model does not have access to the ground truth, tokens generated by the model itself are instead used to make the next prediction.
This discrepancy between training and test leads to the issue that mistakes in prediction can quickly accumulate.
Recent efforts have been made to alleviate the issue, many of which resort to the reinforcement learning (RL) techniques BID24 BID2 BID8 .
For example, BID24 adopt policy gradient BID29 that avoids the training/test discrepancy by using the same decoding strategy.
However, RL-based approaches for sequence generation can face challenges of prohibitively poor sample efficiency and high variance.
For more practical training, a diverse set of methods has been developed that are in a middle ground between the two paradigms of MLE and RL.
For example, RAML adds reward-aware perturbation to the MLE data examples; SPG BID8 leverages reward distribution for effective sampling of policy gradient.
Other approaches such as data noising BID34 ) also show improved results.In this paper, we establish a unified perspective of the broad set of learning algorithms.
Specifically, we present a generalized entropy regularized policy optimization framework, and show that the apparently diverse algorithms, such as MLE, RAML, SPG, and data noising, can all be re-formulated as special instances of the framework, with the only difference being the choice of reward and the values of a couple of hyperparameters ( FIG0 ).
In particular, we show MLE is equivalent to using a delta-function reward that assigns 1 to samples that exactly match data examples while −∞ to any other samples.
Such extremely restricted reward has literally disabled any exploration of the model beyond training data, yielding the exposure bias.
Other algorithms essentially use rewards that are more smooth, and also leverage model distribution for exploration, which generally results in a larger effective exploration space, more difficult training, and better test-time performance.Besides the new understandings of the existing algorithms, the unified perspective also facilitates to develop new algorithms for improved learning.
We present an example new algorithm that, as training proceeds, gradually expands the exploration space by annealing the reward and hyperparameter values.
The annealing in effect dynamically interpolates among the existing algorithms.
Experiments on machine translation and text summarization show the interpolation algorithm achieves significant improvement over the various existing methods.
We have presented a unified perspective of a variety of well-used learning algorithms for sequence generation.
The framework is based on a generalized entropy regularized policy optimization formulation, and we show these algorithms are mathematically equivalent to specifying certain hyperparameter configurations in the framework.
The new principled treatment provides systematic understanding and comparison among the algorithms, and inspires further enhancement.
The proposed interpolation algorithm shows consistent improvement in machine translation and text summarization.
We would be excited to extend the framework to other settings such as robotics and game environments.A POLICY GRADIENT & MIXER BID24 made an early attempt to address the exposure bias problem by exploiting the policy gradient algorithm BID29 .
Policy gradient aims to maximizes the expected reward: DISPLAYFORM0 where R P G is usually a common reward function (e.g., BLEU).
Taking gradient w.r.t θ gives: DISPLAYFORM1 We now reveal the relation between the ERPO framework we present and the policy gradient algorithm.Starting from the M-step of Eq.(2) and setting (α = 1, β = 0) as in SPG (section 3.4), we use p θ n as the proposal distribution and obtain the importance sampling estimate of the gradient (we omit the superscript n for notation simplicity): DISPLAYFORM2 where Z θ = y exp{log p θ + R} is the normalization constant of q, which can be considered as adjusting the step size of gradient descent.We can see that Eq.(12) recovers Eq.(11) if we further set R = log R P G , and omit the scaling factor Z θ . In
other words, policy gradient can be seen as a special instance of the general ERPO framework with (R = log R P G , α = 1, β = 0) and with Z θ omitted.The MIXER algorithm BID24 incorporates an annealing strategy that mixes between MLE and policy gradient training. Specifically
, given a ground-truth example y * , the first m tokens y * 1:m are used for evaluating MLE loss, and starting from step m + 1, policy gradient objective is used. The m value
decreases as training proceeds. With the relation
between policy gradient and ERPO as established above, MIXER can be seen as a specific instance of the proposed interpolation algorithm (section 4) that follows a restricted annealing strategy for token-level hyperparameters (λ 1 , λ 2 , λ 3 ). That is, for t <
m in Eq.4 (i.e.,the first m steps), (λ 1 , λ 2 , λ 3 ) is set to (0, 0, 1) and c = 1, namely the MLE training; while for t > m, (λ 1 , λ 2 , λ 3 ) is set to (0.5, 0.5, 0) and c = 2.

assistant: text: A unified perspective of various learning algorithms for sequence generation, such as MLE, RL, RAML, data noising, etc.