Best of both worlds: Stochastic & adversarial best-arm identification
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 ...
| Authors | Yasin Abbasi-Yadkori, Peter L. Bartlett, Victor Gabillon et al. |
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| Primary category | stat.ML |
| Published | 16 April 2026 |
| Last updated at source | 16 April 2026 |
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