Softmax Q-Distribution Estimation for Structured Prediction: A Theoretical Interpretation for RAML
This work provides a theoretical foundation for RAML, benefiting researchers in structured prediction by clarifying its Bayesian connections, though it is incremental as it builds on existing empirical successes.
The paper tackles the lack of theoretical understanding of Reward Augmented Maximum Likelihood (RAML) in structured prediction by introducing softmax Q-distribution estimation, which interprets RAML as approximating a Bayes decision boundary and shows equivalence with controlled error via temperature. Experiments on synthetic and real tasks, including image captioning and machine translation, demonstrate notable improvements over maximum likelihood baselines.
Reward augmented maximum likelihood (RAML), a simple and effective learning framework to directly optimize towards the reward function in structured prediction tasks, has led to a number of impressive empirical successes. RAML incorporates task-specific reward by performing maximum-likelihood updates on candidate outputs sampled according to an exponentiated payoff distribution, which gives higher probabilities to candidates that are close to the reference output. While RAML is notable for its simplicity, efficiency, and its impressive empirical successes, the theoretical properties of RAML, especially the behavior of the exponentiated payoff distribution, has not been examined thoroughly. In this work, we introduce softmax Q-distribution estimation, a novel theoretical interpretation of RAML, which reveals the relation between RAML and Bayesian decision theory. The softmax Q-distribution can be regarded as a smooth approximation of the Bayes decision boundary, and the Bayes decision rule is achieved by decoding with this Q-distribution. We further show that RAML is equivalent to approximately estimating the softmax Q-distribution, with the temperature $τ$ controlling approximation error. We perform two experiments, one on synthetic data of multi-class classification and one on real data of image captioning, to demonstrate the relationship between RAML and the proposed softmax Q-distribution estimation method, verifying our theoretical analysis. Additional experiments on three structured prediction tasks with rewards defined on sequential (named entity recognition), tree-based (dependency parsing) and irregular (machine translation) structures show notable improvements over maximum likelihood baselines.