The Benefits of Being Categorical Distributional: Uncertainty-aware Regularized Exploration in Reinforcement Learning

The theoretical advantages of distributional reinforcement learning~(RL) over classical RL remain elusive despite its remarkable empirical performance. Starting from Categorical Distributional RL~(CDRL), we attribute the potential superiority of distributional RL to a derived distribution-matching regularization by applying a return density function decomposition technique. This unexplored regularization in the distributional RL context is aimed at capturing additional return distribution information regardless of only its expectation, contributing to an augmented reward signal in the policy optimization. Compared with the entropy regularization in MaxEnt RL that explicitly optimizes the policy to encourage the exploration, the resulting regularization in CDRL implicitly optimizes policies guided by the new reward signal to align with the uncertainty of target return distributions, leading to an uncertainty-aware exploration effect. Finally, extensive experiments substantiate the importance of this uncertainty-aware regularization in distributional RL on the empirical benefits over classical RL.