  Many modern approaches to offline Reinforcement Learning (RL) utilize
behavior regularization, typically augmenting a model-free actor critic
algorithm with a penalty measuring divergence of the policy from the offline
data. In this work, we propose an alternative approach to encouraging the
learned policy to stay close to the data, namely parameterizing the critic as
the log-behavior-policy, which generated the offline data, plus a state-action
value offset term, which can be learned using a neural network. Behavior
regularization then corresponds to an appropriate regularizer on the offset
term. We propose using a gradient penalty regularizer for the offset term and
demonstrate its equivalence to Fisher divergence regularization, suggesting
connections to the score matching and generative energy-based model literature.
We thus term our resulting algorithm Fisher-BRC (Behavior Regularized Critic).
On standard offline RL benchmarks, Fisher-BRC achieves both improved
performance and faster convergence over existing state-of-the-art methods.
