Measurable Monte Carlo Search Error Bounds

John Mern; Mykel J. Kochenderfer

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arXiv · 2106.04715

Measurable Monte Carlo Search Error Bounds

John Mern·Mykel J. Kochenderfer

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Abstract

Monte Carlo planners can often return sub-optimal actions, even if they are guaranteed to converge in the limit of infinite samples. Known asymptotic regret bounds do not provide any way to measure confidence of a recommended action at the conclusion of search. In this work, we prove bounds on the sub-optimality of Monte Carlo estimates for non-stationary bandits and Markov decision processes. These bounds can be directly computed at the conclusion of the search and do not require knowledge of the true action-value. The presented bound holds for general Monte Carlo solvers meeting mild convergence conditions. We empirically test the tightness of the bounds through experiments on a multi-armed bandit and a discrete Markov decision process for both a simple solver and Monte Carlo tree search.

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John Mern, Mykel J. Kochenderfer. 2021-06-08. Measurable Monte Carlo Search Error Bounds. https://arxiv.org/abs/2106.04715

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