  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
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/.
