  Due to the inability to interact with the environment, offline reinforcement
learning (RL) methods face the challenge of estimating the Out-of-Distribution
(OOD) points. Existing methods for addressing this issue either control policy
to exclude the OOD action or make the $Q$ function pessimistic. However, these
methods can be overly conservative or fail to identify OOD areas accurately. To
overcome this problem, we propose a Constrained Policy optimization with
Explicit Behavior density (CPED) method that utilizes a flow-GAN model to
explicitly estimate the density of behavior policy. By estimating the explicit
density, CPED can accurately identify the safe region and enable optimization
within the region, resulting in less conservative learning policies. We further
provide theoretical results for both the flow-GAN estimator and performance
guarantee for CPED by showing that CPED can find the optimal $Q$-function
value. Empirically, CPED outperforms existing alternatives on various standard
offline reinforcement learning tasks, yielding higher expected returns.
