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arXiv · 2211.15602

Upper Bounds for All and Max-gain Policy Iteration Algorithms on Deterministic MDPs

Ritesh Goenka·Eashan Gupta·Sushil Khyalia·Pratyush Agarwal·Mulinti Shaik Wajid·Shivaram Kalyanakrishnan
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Abstract

Policy Iteration (PI) is a widely used family of algorithms to compute optimal policies for Markov Decision Problems (MDPs). We derive upper bounds on the running time of PI on Deterministic MDPs (DMDPs): the class of MDPs in which every state-action pair has a unique next state. Our results include a non-trivial upper bound that applies to the entire family of PI algorithms; another to all "max-gain" switching variants; and affirmation that a conjecture regarding Howard's PI on MDPs is true for DMDPs. Our analysis is based on certain graph-theoretic results, which may be of independent interest.

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Ritesh Goenka, Eashan Gupta, Sushil Khyalia, Pratyush Agarwal, Mulinti Shaik Wajid, Shivaram Kalyanakrishnan. 2022-11-28. Upper Bounds for All and Max-gain Policy Iteration Algorithms on Deterministic MDPs. https://arxiv.org/abs/2211.15602

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