发表机构
Tsinghua University; Harvard Business School（清华大学; 哈佛商学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对有限时间范围老虎机问题，提出正则化贪心算法，推导其有限时间范围遗憾包络并校准参数，实验显示其性能优于或匹配当前最优算法，为该问题提供有效方案。
AI 中文摘要
各机构越来越依赖序贯实验来优化决策。多臂老虎机文献已提出具有强渐近遗憾保证的算法，但许多实际应用在有限且外部给定的时间范围内运行。受有限时间范围设定的启发，我们针对多臂伯努利老虎机开发了一类正则化贪心算法。我们推导了正则化贪心老虎机的首个有限时间范围遗憾包络，表明有限时间范围遗憾可分解为暂态探索成本和次优收敛项，后者随正则化强度呈指数衰减。该特性为正则化参数提供了原则性校准规则，且作为极限情况，为经典贪心策略提供了更精确的遗憾保证。在大量数值实验中，经校准的正则化贪心策略始终与当前最优算法表现相当或更优。这些结果表明，正则化贪心策略可为有限时间范围老虎机问题提供有效解决方案。
英文摘要
Organizations increasingly rely on sequential experimentation to improve decision-making. While the multi-armed bandit literature has developed algorithms with strong asymptotic regret guarantees, many practical applications operate over finite and externally imposed horizons. Motivated by the finite-horizon setting, we develop a class of regularized greedy algorithms for multi-armed Bernoulli bandits. We derive the first finite-horizon regret envelopes for regularized greedy bandits, showing that finite-horizon regret decomposes into transient exploration costs and a suboptimal convergence term that decays exponentially with the regularization strength. This characterization yields principled calibration rules for the regularization parameters and, as a limiting case, sharper regret guarantees for the classical greedy policy. Across extensive numerical experiments, calibrated regularized greedy policies consistently match or outperform state-of-the-art algorithms. These results suggest that regularized greedy policies can provide an effective approach for finite-horizon bandit problems.
Comments122 pages, 3 figures, submitted to Management Science and under peer review
