Text Generation by Learning from Demonstrations

1 INTRODUCTION . A dominant approach to text generation is to use autoregressive models learned by maximum likelihood estimation ( MLE ) on supervised data . However , this approach introduces two well-known discrepancies between training and evaluation objectives that lead to undesired generations . First , the training loss is negative log-likelihood , whereas the evaluation is based on human judgment of the output quality . Under model misspecification , MLE tends to over-generalize , assigning large probability mass to both high-quality and low-quality sequences ( Huszár , 2015 ; Simon et al. , 2019 ) . Therefore , in practice , we must carefully select the decoding algorithms to produce high-quality outputs . Second , during training , the autoregressive model conditions on the gold history/prefix ; however , at inference time it conditions on model-generated history . This is known as the exposure bias problem ( Ranzato et al. , 2016 ; Bengio et al. , 2015 ) . In the worst case , one incorrect prediction can produce a low-probability prefix under the gold data distribution , and errors compound in each of the following steps ( Ross et al. , 2011 ) . In practice , prior work has observed problems such as repetition and hallucination partly due to exposure bias ( Holtzman et al. , 2020 ; Wang & Sennrich , 2020 ) . We aim to bridge the gap between training and evaluation in this paper . To match training and evaluation objectives , ideally we should maximize output quality given model-generated histories . This corresponds to the reinforcement learning ( RL ) objective : maximizing the expected reward ( quality ) over trajectories ( sequences ) induced by the policy ( model ) . However , optimizing this objective is notoriously difficult . Prior RL approaches mainly focus on fine-tuning a learned model to optimize sequence-level metrics such as BLEU ( Papineni et al. , 2002 ) , but empirically it remains unclear if RL is beneficial to text generation ( Wu et al. , 2018 ; Choshen et al. , 2020 ) . Note that many challenges in RL arise from exploring an exponentially large space of sequences , with sparse rewards only on those close to the reference . We thus propose to learn from only the reference sequences without interaction ( i.e. , the offline setting ) . Specifically , we use off-policy policy gradient with importance weighting ( Hastings , 1970 ; Hachiya et al. , 2009 ; Parshakova et al. , 2019 ) , where training examples with higher probability under the model are weighted higher . Further , our reward functions approximate human judgment of the output quality by estimating how likely a human would have generated a sequence . We call our algorithm GOLD ( Generation by Off-policy Learning from Demonstrations ) . Results on news summarization , question generation , and machine translation show that GOLD leads to better model performance than MLE and RL fine-tuning by both task metrics and human-rated quality . Further , our analysis shows that GOLD learns high-precision models that are less sensitive to decoding algorithms . In addition , it alleviates exposure bias : the output quality does not degrade much as generation length increases . 2 FROM MLE TO RL FRAMEWORK . MLE training . Given a context x such as a document , we want to generate a sequence of tokens y = ( y0 , . . . , yT ) , where yi comes from a vocabulary V . The generator is modeled by a conditional probability distribution parametrized by θ : pθ ( y | x ) = ∏T t=0 pθ ( yt | y0 : t−1 , x ) , where y0 : t−1 denotes the prefix y0 , . . . , yt−1 . Let phuman ( y | x ) denote the data-generating distribution . Using MLE , the loss function is L ( θ ) = −Ey∼phuman [ T∑ t=0 log pθ ( yt | y0 : t−1 , x ) ] . ( 1 ) At inference time , we generate tokens sequentially according to pθ . Evaluation . In practice , the quality of an output often relies on task-specific metrics such as fluency , correctness , and interestingness . Here for generality we consider perceptual quality ( Huszár , 2015 ; Hashimoto et al. , 2019 ) which measures how likely a human would have generated the output given the context , i.e. , phuman ( y | x ) . Thus the evaluation metric is Ey∼pθ [ T∑ t=0 log phuman ( yt | y0 : t−1 , x ) ] . ( 2 ) Comparing ( 1 ) and ( 2 ) , we see that the training objective encourages high recall : the model must put probability mass on all human-generated sequences . In contrast , the evaluation metric encourages high precision : all outputs from the model must be of high quality . Unfortunately , directly optimizing the evaluation metric is impossible because phuman is unknown and the expectation is difficult to estimate . We therefore develop a training objective that closely approximates ( 2 ) in the RL framework . RL formulation . Let ’ s consider generation as a sequential decision-making process . At each time step t , the policy πθ takes an action at ∈ V , transits to the next state st+1 = ( y0 : t , x ) , and receives a reward rt . The policy corresponds to the generation model : πθ ( at | st ) = pθ ( at | y0 : t−1 , x ) . We can thus represent a sequence as a trajectory τ = ( s0 , a0 , r0 , . . . , sT , aT , rT ) . The set of trajectories derived from the training data is called demonstrations which show the desired behavior of a policy . The RL objective is to maximize J ( θ ) = Eτ∼πθ [ ∑T t=0 γ trt ] , where γ ∈ ( 0 , 1 ] is the discount factor , and πθ ( τ ) denotes the distribution of τ induced by πθ . If we knew oracle rewards rt = phuman ( at | st ) , then this objective would be exactly the evaluation metric we want to optimize . Next , we describe how to optimize J ( θ ) with reward functions that approximate phuman . 3 APPROACH . 3.1 OFF-POLICY POLICY GRADIENT . Policy gradient . A straightforward way to optimize J ( θ ) is policy gradient ( PG ) ( Williams , 1992 ; Sutton et al. , 2000 ) . The gradient is given by ∇θJ ( θ ) = Eτ∼πθ [ ∑ t ∇θ log πθ ( at | st ) Q̂ ( st , at ) ] , ( 3 ) where Q̂ ( st , at ) = ∑T t′=t γ t′−trt′ is the estimated return from state st . The expectation is estimated by Monte Carlo samples from πθ . In text generation , the return Q̂ ( st , at ) is often a sequence-level reward such as BLEU . In practice , the policy is likely to get stuck in a region of zero reward during training , generating gibberish without receiving any learning signal ( Li et al. , 2018 ; Keneshloo et al. , 2019 ) . A common remedy is to initialize the policy with the MLE solution and/or interleave with MLE gradient update during PG . However , this would bias the parameters towards the MLE solution , thus often leads to marginal gains in practice ( Wu et al. , 2018 ; Choshen et al. , 2020 ) . Offline learning . To avoid zero-reward regions , we would like to reduce interaction with the environment and stay close to the demonstrated trajectories . In the extreme case , the policy is learned solely from the static demonstrations without additional interaction with the environment , which is referred to as the offline setting . While it is in general a more challenging problem , we argue that the offline setting is appropriate for text generation ( Serban et al. , 2017 ; Jaques et al. , 2019 ) . First , the environment dynamics is known : once a token is generated , we deterministically transition to the next state with the additional token appended to the prefix ; no interaction is needed to learn the environment . Second , while exploration may lead to high-quality sequences different from the reference , we lack a good reward function to identify them ( Novikova et al. , 2017 ; Aharoni & Goldberg , 2018 ; Clark et al. , 2019 ) . Therefore , the benefit of exploration in text generation is limited . In the offline setting , we can not estimate the expected return of πθ by sampling trajectories from it , and must use trajectories from a different behavioral policy πb , known as off-policy learning in RL . A common technique to estimate expectations under one distribution πθ given samples from a different distribution πb is importance sampling , which leads to the following unbiased estimator of the gradient ( Precup et al. , 2000 ) : Eτ∼πb [ ∑ t wt∇θ log πθ ( at | st ) Q̂ ( st , at ) ] , with importance weights wt = ∏t t′=0 πθ ( at′ |st′ ) πb ( at′ |st′ ) . Approximations . Computing the importance weights above requires multiplying per-action importance weight over multiple time steps . In practice , we have found that it is sensitive to optimization hyperparameters and takes longer to converge . Therefore , we use the per-action approximation : wt ≈ πθ ( at|st ) πb ( at|st ) . This corresponds to optimizing the expected return under the off-policy state distribution induced by πb and the on-policy action distribution of πθ . Although this estimator is biased , empirically it has been shown to reduce variance and work reasonably well if πb and πθ are close ( Serban et al. , 2017 ; Levine et al. , 2020 ) . Another obstacle is that we do not know πb which produced the demonstrationsD = { ( x ( i ) , y ( i ) ) } Ni=1 . One option is to estimate πb onD . Here we take a simpler approach that uses the empirical distribution : πb ( τ ) ≈ 1/N for τ ∈ D and 0 otherwise . As a result , the denominator in wt is a constant and can be ignored in optimization . Our final approximated gradient has the form : ∇θJ ( θ ) ≈ N∑ i=1 T∑ t=0 πθ ( a i t | sit ) ∇θ log πθ ( ait | sit ) Q̂ ( sit , ait ) , ( 4 ) where the superscript i represents the ith trajectory . Compared with the MLE gradient : ∑N i=1 ∑T t=0∇θ log πθ ( ait | sit ) , our gradient ( 4 ) upweights actions with high return and actions preferred by the current policy πθ . Intuitively , it encourages the learning algorithm to focus on “ easy ” examples ( high likelihood under the model ) which improves precision . 3.2 REWARD . Let R be the reward function such that rt = R ( st , at ) . To optimize the perceptual quality of a sequence ( see ( 2 ) ) , we want R ( s , a ) to approximate phuman ( a | s ) , i.e. , how likely humans would have generated a given s. In general , it is hard to develop a reliable reward function for text generation tasks because it must work well for a large set of possible generations . In the offline setting , however , we can restrict the domain of R to state-action pairs on the demonstrations . Next , we propose three reward functions . δ-reward . An obvious choice is a sequence-level reward , which considers all demonstrations to be equally good and assigns zero reward to any other outputs . Formally , Rδ ( st , at ) def = { 1 , if t = T and ( s0 : T , a0 : T ) ∈ D 0 , otherwise ( 5 ) where a reward of one is received in the terminal state for any trajectory in the demonstrations . Estimated phuman . In text generation tasks , an input often has many correct outputs and the reference may be an uncommon output that contains rare words or has complex syntax . To account for different likelihood of the references , we estimate the probability of each reference by minimizing KL ( phuman‖q ) , where q ( a | s ) approximates phuman ( a | s ) . This is equivalent to finding the MLE solution ( denoted by pMLE ) .1 Importantly , pMLE is a reasonable approximation to phuman when restricted to the demonstrations . It is not a good reward function in general , however ; it can assign large probability mass to low-quality outputs . Given the estimated perceptual quality pMLE ( a | s ) , we define two reward functions . Our first reward function corresponds to a product of probabilities when summed over the trajectory : Rp ( s , a ) def = log pMLE ( a | s ) . ( 6 ) Assuming γ = 1 , the return at time step t is Q̂t ( st , at ) = ∑T t′=t log pMLE ( at | st ) . Thus a sequence has high reward only if every word has high likelihood under pMLE . To allow for partial credits even if bad actions are taken at certain steps , we define another reward function corresponding to the sum of probabilities : Rs ( s , a ) def = pMLE ( a | s ) . ( 7 ) The return Q̂ ( st , at ) = ∑T t′=t pMLE ( at | st ) , thus the policy can recover from bad decisions if the subsequent actions receive high reward . 3.3 THE GOLD ALGORITHM Algorithm 1 : GOLD 1 πθ ← pMLE , π̃θ ← pMLE 2 for step = 1 , 2 , . . . , M do 3 Sample a minibatch B = { ( xi , yi ) } |B|i=1 4 foreach ( sit , ait ) do 5 Compute importance weights max ( u , π̃θ ) , and compute returns Q̂ ( sit , a i t ) − b 6 Update θ by ( 4 ) using gradient descent 7 if step % k = 0 then π̃θ ← πθ 8 Return : πθ Our full algorithm based on off-policy PG is shown in Algorithm 1 . For importance weights πθ ( a | s ) , to avoid drastic changes , we initialize πθ with the MLE solution . In addition , we compute the importance weights by a weighting policy π̃θ that synchronizes with πθ periodically so that the weights do not change frequently between updates . We also lower-bound the importance weight by a small number u . Another source of variance comes from policy gradients . Since our return is computed from a sum or product of probabilities ( ( 6 ) and ( 7 ) ) , we truncate the future trajectory after five steps . We follow the common practice to subtract a baseline b from the return to reduce variance ; moreover , to avoid negative reward on the demonstrations ( after subtracting baseline ) , we lower-bound pMLE in ( 6 ) and ( 7 ) by a small number c. In practice , GOLD is easy to implement ; further , given an existing pMLE , the GOLD-training stage usually takes less time than MLE . The code is available.2 .

Summary: This paper formalizes training of conditional text generation models as an off-policy RL objective, specifically, in the limit case where samples are only obtained from the training data. The motivation behind this is that MLE objective optimizes recall -i.e. increasing the prob of all correct sequences that could be generated by humans as an output to a certain input context. While for certain tasks such as MT or summarization it is often sufficient to focus training to generate 1 single correct Translation or summary (see cons: for comments on the effect of this on sample diversity).  Therefore explorations in traditional PG by generating examples from an auto-reg model is unnecessary in this context. Therefore, using importance sampling, PG objective \E_{x \sim \pi_\theta} is modified to \E_{x \sim \pi_{data}} with the incorporation of the importance ratio and given a uniform sample probability of the training examples. As shown in eq(4), The gradient updates from this loss are identical to the standard MLE loss reweighted by the global reward and the current model probability of the training example, enforcing the model's current belief of the training data. This aligns with the previous intuition of enhancing precision on the expense of recall. Given this formulization this work experiments with three types of rewards: a constant reward and 2 MLE based rewards.