UDQL: Bridging The Gap between MSE Loss and The Optimal Value Function in Offline Reinforcement Learning

TL;DR

This paper analyzes the overestimation issue caused by MSE in offline RL value estimation, proposes a new underestimated operator to counteract it, and demonstrates improved performance on D4RL benchmarks.

Contribution

It introduces a novel Bellman underestimated operator with proven contraction properties to mitigate overestimation in offline RL.

Findings

Theoretical upper bound of overestimation error is derived.

The proposed method outperforms state-of-the-art offline RL algorithms on D4RL tasks.

Theoretical analysis confirms the effectiveness of the underestimated operator.

Abstract

The Mean Square Error (MSE) is commonly utilized to estimate the solution of the optimal value function in the vast majority of offline reinforcement learning (RL) models and has achieved outstanding performance. However, we find that its principle can lead to overestimation phenomenon for the value function. In this paper, we first theoretically analyze overestimation phenomenon led by MSE and provide the theoretical upper bound of the overestimated error. Furthermore, to address it, we propose a novel Bellman underestimated operator to counteract overestimation phenomenon and then prove its contraction characteristics. At last, we propose the offline RL algorithm based on underestimated operator and diffusion policy model. Extensive experimental results on D4RL tasks show that our method can outperform state-of-the-art offline RL algorithms, which demonstrates that our theoretical analysis and underestimation way are effective for offline RL tasks.