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It has been recently shown in the literature that the sample averages fromonline learning experiments are biased when used to estimate the mean reward.To correct the bias, off-policy evaluation methods, including importancesampling and doubly robust estimators, typically calculate the conditionalpropensity score, which is ill-defined for non-randomized policies such as UCB.This paper provides a procedure to debias the samples using bootstrap, whichdoesn't require the knowledge of the reward distribution and can be applied toany adaptive policies. Numerical experiments demonstrate the effective biasreduction for samples generated by popular multi-armed bandit algorithms suchas Explore-Then-Commit (ETC), UCB, Thompson sampling (TS) and $\epsilon$-greedy(EG). We analyze and provide theoretical justifications for the procedure underthe ETC algorithm, including the asymptotic convergence of the bias decay ratein the real and bootstrap worlds.

Debiasing Samples from Online Learning Using Bootstrap