Offline Reinforcement Learning with Closed-Form Policy Improvement Operators

Jiachen Li, Edwin Zhang, Ming Yin, Qinxun Bai, Yu-Xiang Wang, William Yang Wang

Keywords: Offline Reinforcement Learning algorithms, Deep Reinforcement Learning

TL;DR: We proposed a closed-form policy improvement operator and modeled the behavior policies as a Gaussian Mixture.

Abstract: Behavior constrained policy optimization has been demonstrated to be a successful paradigm for tackling Offline Reinforcement Learning. By exploiting historical transitions, a policy is trained to maximize a learned value function while constrained by the behavior policy to avoid a significant distributional shift. In this paper, we propose our closed-form policy improvement operators. We make a novel observation that the behavior constraint naturally motivates the use of first-order Taylor approximation, leading to a linear approximation of the policy objective. Additionally, as practical datasets are usually collected by heterogeneous policies, we model the behavior policies as a Gaussian Mixture and overcome the induced optimization difficulties by leveraging the LogSumExp's lower bound and Jensen's Inequality, giving rise to a closed-form policy improvement operator. We instantiate an offline RL algorithm with our novel policy improvement operator and empirically demonstrate its effectiveness over state-of-the-art algorithms on the standard D4RL benchmark.

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