Multimodal Bandits: Regret Lower Bounds and Optimal Algorithms

William Réveillard; Richard Combes

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arXiv · 2510.25811

Multimodal Bandits: Regret Lower Bounds and Optimal Algorithms

William Réveillard·Richard Combes

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Abstract

We consider a stochastic multi-armed bandit problem with i.i.d. rewards where the expected reward function is multimodal with at most m modes. We propose the first known computationally tractable algorithm for computing the solution to the Graves-Lai optimization problem, which in turn enables the implementation of asymptotically optimal algorithms for this bandit problem. The code for the proposed algorithms is publicly available at https://github.com/wilrev/MultimodalBandits

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William Réveillard, Richard Combes. 2025-10-29. Multimodal Bandits: Regret Lower Bounds and Optimal Algorithms. https://arxiv.org/abs/2510.25811

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