An Analysis of Categorical Distributional Reinforcement Learning

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Mark Rowland, Marc Bellemare, Will Dabney, Remi Munos, Yee Whye Teh ;
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:29-37, 2018.

Abstract

Distributional approaches to value-based reinforcement learning model the entire distribution of returns, rather than just their expected values, and have recently been shown to yield state-of-the-art empirical performance. This was demonstrated by the recently proposed C51 algorithm, based on categorical distributional reinforcement learning (CDRL) [Bellemare et al., 2017]. However, the theoretical properties of CDRL algorithms are not yet well understood. In this paper, we introduce a framework to analyse CDRL algorithms, establish the importance of the projected distributional Bellman operator in distributional RL, draw fundamental connections between CDRL and the Cramer distance, and give a proof of convergence for sample-based categorical distributional reinforcement learning algorithms.

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