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arXiv · 2502.13467

On the Sublinear Regret of Continuous K-Max Bandits

Yu Chen·Siwei Wang·Longbo Huang·Wei Chen
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Abstract

The $K$-Max combinatorial multi-armed bandit problem arises in applications such as recommendation and distributed decision making, where the reward is determined by the maximum outcome among $K$ selected arms. When outcomes are continuous and only the maximum value together with the winner's index is observed, this problem introduces unprecedented difficulties including discretization errors, non-deterministic tie-breaking, and severe estimation biases. To overcome these barriers, we introduce DCK-UCB, an efficient algorithm combining adaptive discretization with bias-corrected confidence bounds. We prove that DCK-UCB achieves a $\widetilde{O}(T^{3/4})$ regret bound, the first sublinear guarantee in this setting. Numerical experiments show strong performance over baseline methods. Furthermore, for the specific case of exponential distributions under full-bandit feedback, we propose the MLE-Exp algorithm that attains a near-optimal $\widetilde{O}(\sqrt{T})$ regret bound. This work establishes fundamental theoretical guarantees and provides a powerful algorithmic solution for continuous combinatorial bandits.

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Yu Chen, Siwei Wang, Longbo Huang, Wei Chen. 2025-02-19. On the Sublinear Regret of Continuous K-Max Bandits. https://arxiv.org/abs/2502.13467

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