[PDF] On the Existence of a Complexity in Fixed Budget Bandit Identification-论文阅读讨论-ReadPaper

摘要

In fixed budget bandit identification, an algorithm sequentially observessamples from several distributions up to a given final time. It then answers aquery about the set of distributions. A good algorithm will have a smallprobability of error. While that probability decreases exponentially with thefinal time, the best attainable rate is not known precisely for mostidentification tasks. We show that if a fixed budget task admits a complexity,defined as a lower bound on the probability of error which is attained by asingle algorithm on all bandit problems, then that complexity is determined bythe best non-adaptive sampling procedure for that problem. We show that thereis no such complexity for several fixed budget identification tasks includingBernoulli best arm identification with two arms: there is no single algorithmthat attains everywhere the best possible rate.

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