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Conference Papers Year : 2018

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

Alan Malek
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Michal Valko


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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Dates and versions

hal-01808948 , version 1 (06-06-2018)
hal-01808948 , version 2 (12-07-2018)
hal-01808948 , version 3 (16-07-2018)
hal-01808948 , version 4 (23-07-2018)
hal-01808948 , version 5 (19-07-2021)
hal-01808948 , version 6 (31-07-2023)


  • 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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