Regularized Policies are Reward Robust

TL;DR

This paper reveals that entropic regularization in reinforcement learning acts as a form of reward robustness, making policies optimal under worst-case adversarial rewards, thus providing a new perspective on exploration and regularization effects.

Contribution

The authors derive a dual formulation showing regularized RL as an adversarial reward problem, connecting regularization to robust policy optimization.

Findings

Regularized policies are equivalent to solving a worst-case adversarial reward problem.

Entropic regularization can be interpreted as a robustness mechanism against reward perturbations.

The framework applies to various regularization schemes beyond entropy.

Abstract

Entropic regularization of policies in Reinforcement Learning (RL) is a commonly used heuristic to ensure that the learned policy explores the state-space sufficiently before overfitting to a local optimal policy. The primary motivation for using entropy is for exploration and disambiguating optimal policies; however, the theoretical effects are not entirely understood. In this work, we study the more general regularized RL objective and using Fenchel duality; we derive the dual problem which takes the form of an adversarial reward problem. In particular, we find that the optimal policy found by a regularized objective is precisely an optimal policy of a reinforcement learning problem under a worst-case adversarial reward. Our result allows us to reinterpret the popular entropic regularization scheme as a form of robustification. Furthermore, due to the generality of our results, we apply to other existing regularization schemes. Our results thus give insights into the effects of regularization of policies and deepen our understanding of exploration through robust rewards at large.