Tight (Lower) Bounds for the Fixed Budget Best Arm Identification Bandit Problem

@inproceedings{Carpentier2016TightB,
  title={Tight (Lower) Bounds for the Fixed Budget Best Arm Identification Bandit Problem},
  author={Alexandra Carpentier and Andrea Locatelli},
  booktitle={COLT},
  year={2016}
}
We consider the problem of best arm identification with a fixed budget T , in theK-armed stochastic bandit setting, with arms distribution defined on [0, 1]. We prove that any bandit strategy, for at least one bandit problem characterized by a complexityH , will misidentify the best arm with probability lower bounded by exp ( − T log(K)H ) , whereH is the sum for all sub-optimal arms of the inverse of the squared gaps. Our result disproves formally the general belief coming from results in the… CONTINUE READING
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