Multimodal Bandits: Regret Lower Bounds and Optimal Algorithms

• URL: http://arxiv.org/abs/2510.25811v1
• Date: Wed, 29 Oct 2025 12:32:07 GMT
• Title: Multimodal Bandits: Regret Lower Bounds and Optimal Algorithms
• Authors: William Réveillard, Richard Combes,
• Abstract summary: We consider a multi-armed bandit problem with i.i.d. rewards where the expected reward function is multimodal with at most m modes.<n>We propose the first known computationally tractable solution to the Graves-Lai optimization problem, which in turn enables the implementation of algorithmally optimal algorithms for this bandit problem.
• Score: 7.534196213324318
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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