Importance Weighted Actor-Critic for Optimal Conservative Offline Reinforcement Learning

Abstract

We propose A-Crab (Actor-Critic Regularized by Average Bellman error), a new 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 is practical and achieves the optimal statistical rate of $1/N^{1/2}$—where N is the size of the offline dataset—in converging to the best policy covered in the offline dataset, even when combined with general function approximations.
2. It relies on a weaker average notion of policy coverage (compared to the ℓ∞ single-policy concentrability) that exploits the structure of policy visitations.
3. It outperforms the data-collection behavior policy over a wide-range of hyperparameters and is the first algorithm to do so without solving a minimax optimization problem.