Speedy Categorical Distributional Reinforcement Learning and Complexity Analysis

. In distributional reinforcement learning, the entire distribution of the return instead of just the expected return is modeled. The approach with categorical distributions as the approximation method is well-known in Q-learning, and convergence results have been established in the tabular case. In this work, speedy Q-learning is extended to categorical distributions, a finite-time analysis is performed, and probably approximately correct bounds in terms of the Cram´er distance are established. It is shown that also in the distributional case the new update rule yields faster policy evaluation in comparison to the standard Q-learning one and that the sample complexity is essentially the same as the one of the value-based algorithmic counterpart. Without the need for more state-action-reward samples, one gains significantly more information about the return with categorical distributions. Even though the results do not easily extend to the case of policy control, a slight modification to the update rule yields promising numerical results.