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Best of both worlds: Stochastic & adversarial best-arm identification

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.
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Contributor : Victor Gabillon <>
Submitted on : Monday, July 23, 2018 - 11:13:48 PM
Last modification on : Monday, December 14, 2020 - 5:25:00 PM
Long-term archiving on: : Wednesday, October 24, 2018 - 3:27:40 PM


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  • HAL Id : hal-01808948, version 4


Yasin Abbasi-Yadkori, Peter Bartlett, Victor Gabillon, Alan Malek, Michal Valko. Best of both worlds: Stochastic & adversarial best-arm identification. Conference on Learning Theory, 2018, Stockholm, Sweden. ⟨hal-01808948v4⟩



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