Reinforcement Learning via Fenchel-Rockafellar Duality

TL;DR

This paper reviews Fenchel-Rockafellar convex duality and demonstrates its application to various reinforcement learning problems, providing a unified framework that enables offline policy evaluation, optimization, and policy learning.

Contribution

It offers a unified perspective on applying convex duality to RL, connecting existing results and enabling new methods for offline and online learning.

Findings

Unified treatment of convex duality in RL

Methods for offline policy evaluation and gradient estimation

Framework for policy learning via max-likelihood optimization

Abstract

We review basic concepts of convex duality, focusing on the very general and supremely useful Fenchel-Rockafellar duality. We summarize how this duality may be applied to a variety of reinforcement learning (RL) settings, including policy evaluation or optimization, online or offline learning, and discounted or undiscounted rewards. The derivations yield a number of intriguing results, including the ability to perform policy evaluation and on-policy policy gradient with behavior-agnostic offline data and methods to learn a policy via max-likelihood optimization. Although many of these results have appeared previously in various forms, we provide a unified treatment and perspective on these results, which we hope will enable researchers to better use and apply the tools of convex duality to make further progress in RL.