Residuals-based Offline Reinforcement Learning

TL;DR

This paper introduces a residuals-based framework for offline reinforcement learning that explicitly models estimation errors, providing theoretical guarantees and demonstrating effectiveness in a CartPole environment.

Contribution

It proposes a novel residuals-based Bellman operator and develops an offline deep Q-learning algorithm with finite-sample guarantees.

Findings

The residuals-based Bellman operator is a contraction mapping.

The fixed point of the operator is asymptotically optimal under certain conditions.

The residuals-based offline DQN performs effectively in a stochastic CartPole environment.

Abstract

Offline reinforcement learning (RL) has received increasing attention for learning policies from previously collected data without interaction with the real environment, which is particularly important in high-stakes applications. While a growing body of work has developed offline RL algorithms, these methods often rely on restrictive assumptions about data coverage and suffer from distribution shift. In this paper, we propose a residuals-based offline RL framework for general state and action spaces. Specifically, we define a residuals-based Bellman optimality operator that explicitly incorporates estimation error in learning transition dynamics into policy optimization by leveraging empirical residuals. We show that this Bellman operator is a contraction mapping and identify conditions under which its fixed point is asymptotically optimal and possesses finite-sample guarantees. We further develop a residuals-based offline deep Q-learning (DQN) algorithm. Using a stochastic CartPole environment, we demonstrate the effectiveness of our residuals-based offline DQN algorithm.