Adaptive Monte Carlo via Bandit Allocation

Abstract

We consider the problem of sequentially choos-ing between a set of unbiased Monte Carlo estimators to minimize the mean-squared-error (MSE) of a final combined estimate. By reduc-ing this task to a stochastic multi-armed bandit problem, we show that well developed allocation strategies can be used to achieve an MSE that ap-proaches that of the best estimator chosen in ret-rospect. We then extend these developments to a scenario where alternative estimators have dif-ferent, possibly stochastic costs. The outcome is a new set of adaptive Monte Carlo strategies that provide stronger guarantees than previous approaches while offering practical advantages. 1

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oai:CiteSeerX.psu:10.1.1.746.9293Last time updated on 10/30/2017

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