The Smoothed Complexity of Policy Iteration for Markov Decision Processes

Miranda Christ; Mihalis Yannakakis

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arXiv · 2212.00083

The Smoothed Complexity of Policy Iteration for Markov Decision Processes

Miranda Christ·Mihalis Yannakakis

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Abstract

We show subexponential lower bounds (i.e., $2^{\Omega (n^c)}$) on the smoothed complexity of the classical Howard's Policy Iteration algorithm for Markov Decision Processes. The bounds hold for the total reward and the average reward criteria. The constructions are robust in the sense that the subexponential bound holds not only on the average for independent random perturbations of the MDP parameters (transition probabilities and rewards), but for all arbitrary perturbations within an inverse polynomial range. We show also an exponential lower bound on the worst-case complexity for the simple reachability objective.

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BibTeX RIS

Miranda Christ, Mihalis Yannakakis. 2022-11-30. The Smoothed Complexity of Policy Iteration for Markov Decision Processes. https://arxiv.org/abs/2212.00083

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