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arXiv · 2510.09425

Bandits with Single-Peaked Preferences and Limited Resources

Omer Ben-Porat·Gur Keinan·Rotem Torkan
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Abstract

We study an online stochastic matching problem in which an algorithm sequentially matches $U$ users to $K$ arms, aiming to maximize cumulative reward over $T$ rounds under budget constraints. Without structural assumptions, computing the optimal matching is NP-hard, making online learning computationally infeasible. To overcome this barrier, we focus on single-peaked preferences -- a well-established structure in social choice theory, where users' preferences are unimodal with respect to a common order over arms. We devise an efficient algorithm for the offline budgeted matching problem, and leverage it into an efficient online algorithm with a regret of $\tilde O(UKT^{2/3})$. Our approach relies on a novel PQ tree-based order approximation method. If the single-peaked structure is known, we develop an efficient UCB-like algorithm that achieves a regret bound of $\tilde O(U\sqrt{TK})$.

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Omer Ben-Porat, Gur Keinan, Rotem Torkan. 2025-10-10. Bandits with Single-Peaked Preferences and Limited Resources. https://arxiv.org/abs/2510.09425

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