针对阈值约束的单调老虎机问题，提出最优选臂算法并证明其理论下界。
Threshold-Based Optimal Arm Selection in Monotonic Bandits: Regret Lower Bounds and Algorithms
- 基于阈值τ设计选臂策略，利用臂均值单调性优化决策
- 证明渐近后悔下界仅依赖于τ附近的相邻臂
- 适用于通信、医疗、推荐等需阈值决策的场景
在多臂老虎机问题中，通常目标是识别期望回报最高的臂。本文研究一种基于阈值的老虎机问题，旨在根据臂与预设阈值τ的关系进行选择。考虑多种变体：首个高于τ的臂、第k个高于或低于τ的臂，或最接近τ的臂，在臂均值单调结构下进行分析。推导出渐近后悔下界，表明其仅依赖于τ邻近的臂。该研究受通信网络（信道质量指示分配）、临床给药、能源管理、推荐系统等应用驱动。提出相应算法，并通过蒙特卡洛模拟验证其最优性。本工作扩展了经典老虎机理论，引入阈值约束以实现高效决策。
原文摘要 · Abstract (English)
In multi-armed bandit problems, the typical goal is to identify the arm with the highest reward. This paper explores a threshold-based bandit problem, aiming to select an arm based on its relation to a prescribed threshold \(τ\). We study variants where the optimal arm is the first above \(τ\), the \(k^{th}\) arm above or below it, or the closest to it, under a monotonic structure of arm means. We derive asymptotic regret lower bounds, showing dependence only on arms adjacent to \(τ\). Motivated by applications in communication networks (CQI allocation), clinical dosing, energy management, recommendation systems, and more. We propose algorithms with optimality validated through Monte Carlo simulations. Our work extends classical bandit theory with threshold constraints for efficient decision-making.
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