Journal ArticleOffline Reinforcement Learning with Closed-Form Policy Improvement OperatorsLi, Jiachen and; Zhang, Edwin; Yin, Ming; Bai, Qinxun; Wang, Yu-Xiang; Wang, William YangKrause, Andreas and; Brunskill, Emma; Cho, Kyunghyun; Engelhardt, Barbara; Sabato, Sivan; Scarlett, JonathanBehavior 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 both one-step and iterative offline RL algorithms with our novel policy improvement operators and empirically demonstrate their effectiveness over state-of-the-art algorithms on the standard D4RL benchmark. Our code is available at https://cfpi-icml23.github.io/.ICML 20232023-07-2310466939Proceedings of Machine Learning Research20220485--205282640-3498https://doi.org/2007117; 2003257National Science Foundation