Importance Weighted Actor-Critic for Optimal Conservative Offline Reinforcement Learning

TL;DR

This paper introduces A-Crab, an offline RL algorithm that combines importance sampling with actor-critic methods, achieving optimal convergence rates and better performance under weaker coverage assumptions.

Contribution

A-Crab is a novel offline RL algorithm that achieves the optimal statistical rate and relies on weaker coverage assumptions, improving over existing methods.

Findings

Achieves $1/\sqrt{N}$ convergence rate in policy evaluation.

Outperforms behavior policy across various hyperparameters.

Validates effectiveness through theoretical analysis and experiments.

Abstract

We propose A-Crab (Actor-Critic Regularized by Average Bellman error), a new practical algorithm for offline reinforcement learning (RL) in complex environments with insufficient data coverage. Our algorithm combines the marginalized importance sampling framework with the actor-critic paradigm, where the critic returns evaluations of the actor (policy) that are pessimistic relative to the offline data and have a small average (importance-weighted) Bellman error. Compared to existing methods, our algorithm simultaneously offers a number of advantages: (1) It achieves the optimal statistical rate of $1/\sqrt{N}$ -- where $N$ is the size of offline dataset -- in converging to the best policy covered in the offline dataset, even when combined with general function approximators. (2) It relies on a weaker average notion of policy coverage (compared to the $\ell_\infty$ single-policy concentrability) that exploits the structure of policy visitations. (3) It outperforms the data-collection behavior policy over a wide range of specific hyperparameters. We provide both theoretical analysis and experimental results to validate the effectiveness of our proposed algorithm.