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arXiv · 2003.07337

Is Temporal Difference Learning Optimal? An Instance-Dependent Analysis

Koulik Khamaru·Ashwin Pananjady·Feng Ruan·Martin J. Wainwright·Michael I. Jordan
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Abstract

We address the problem of policy evaluation in discounted Markov decision processes, and provide instance-dependent guarantees on the $\ell_\infty$-error under a generative model. We establish both asymptotic and non-asymptotic versions of local minimax lower bounds for policy evaluation, thereby providing an instance-dependent baseline by which to compare algorithms. Theory-inspired simulations show that the widely-used temporal difference (TD) algorithm is strictly suboptimal when evaluated in a non-asymptotic setting, even when combined with Polyak-Ruppert iterate averaging. We remedy this issue by introducing and analyzing variance-reduced forms of stochastic approximation, showing that they achieve non-asymptotic, instance-dependent optimality up to logarithmic factors.

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Koulik Khamaru, Ashwin Pananjady, Feng Ruan, Martin J. Wainwright, Michael I. Jordan. 2020-03-16. Is Temporal Difference Learning Optimal? An Instance-Dependent Analysis. https://arxiv.org/abs/2003.07337

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