A Distributional Analysis of Sampling-Based Reinforcement Learning Algorithms

• URL: http://arxiv.org/abs/2003.12239v1
• Date: Fri, 27 Mar 2020 05:13:29 GMT
• Title: A Distributional Analysis of Sampling-Based Reinforcement Learning Algorithms
• Authors: Philip Amortila, Doina Precup, Prakash Panangaden, Marc G. Bellemare
• Abstract summary: We present a distributional approach to theoretical analyses of reinforcement learning algorithms for constant step-sizes. We show that value-based methods such as TD($lambda$) and $Q$-Learning have update rules which are contractive in the space of distributions of functions.
• Score: 67.67377846416106
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a distributional approach to theoretical analyses of reinforcement learning algorithms for constant step-sizes. We demonstrate its effectiveness by presenting simple and unified proofs of convergence for a variety of commonly-used methods. We show that value-based methods such as TD($\lambda$) and $Q$-Learning have update rules which are contractive in the space of distributions of functions, thus establishing their exponentially fast convergence to a stationary distribution. We demonstrate that the stationary distribution obtained by any algorithm whose target is an expected Bellman update has a mean which is equal to the true value function. Furthermore, we establish that the distributions concentrate around their mean as the step-size shrinks. We further analyse the optimistic policy iteration algorithm, for which the contraction property does not hold, and formulate a probabilistic policy improvement property which entails the convergence of the algorithm.

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