@inproceedings{abbasi-yadkori2018best,
abstract = {We study bandit best-arm identification with arbitrary and potentially adversarial rewards. A simple random uniform learner obtains the optimal rate of error in the adversarial scenario. However, this type of strategy is suboptimal when the rewards are sampled stochastically. Therefore, we ask: Can we design a learner that performs optimally in both the stochastic and adversarial problems while not being aware of the nature of the rewards? First, we show that designing such a learner is impossible in general. In particular, to be robust to adversarial rewards, we can only guarantee optimal rates of error on a subset of the stochastic problems. We give a lower bound that characterizes the optimal rate in stochastic problems if the strategy is constrained to be robust to adversarial rewards. Finally, we design a simple parameter-free algorithm and show that its probability of error matches (up to log factors) the lower bound in stochastic problems, and it is also robust to adversarial ones.},
author = {Abbasi-Yadkori, Yasin and Bartlett, Peter and Gabillon, Victor and Malek, Alan and Valko, Michal},
booktitle = {Conference on Learning Theory},
title = {{Best of both worlds: Stochastic {\&} adversarial best-arm identification}},
year = {2018}
}