Regret Analysis of Retry-Based Bandits
We provide the first regret analysis of ReMax in stochastic multi-armed bandits. Originally introduced for reinforcement learning, ReMax is motivated by the role of exploration when multiple attempts are allowed, and is closely related to retry-based objectives such as pass@$k$ and max@$k$, which value the best outcome across those attempts. Given a posterior over arm values, ReMax chooses a sampling distribution that maximizes the posterior expected maximum arm value over $M$ virtual draws. For Gaussian rewards with $K$ arms and any fixed integer $M\ge2$, we characterize optimal sampling distributions through an expected-improvement balance condition and prove an $O(\sqrt{(M-1)KT\log T})...
| Authors | Bingkui Tong, Junpei Komiyama, Soichiro Nishimori et al. |
|---|---|
| Primary category | cs.LG |
| Published | 20 May 2026 |
| Last updated at source | 29 September 2026 |
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