Regret Analysis of Retry-Based Bandits

תקציר מקורי באנגליתarXiv:2605.20854v3 Announce Type: replace Abstract: 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 $O(\sqrt{(M-1)KT\log T})$ finite-time bound on expected regret. Our analysi