Abstract
We consider the problem of sequentially choosing between a set of
unbiased Monte Carlo estimators to minimize the mean-squared-error (MSE) of a
final combined estimate.
By reducing this task to a stochastic multi-armed bandit problem,
we show that well developed allocation strategies can be used to achieve
an MSE that approaches that of the best estimator chosen in retrospect.
We then extend these developments to a scenario where alternative estimators
have different, 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.
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