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arXiv 2406.06552q-fin.PMcs.LG
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优化夏普比率：多臂老虎机中的风险调整决策

Optimizing Sharpe Ratio: Risk-Adjusted Decision-Making in Multi-Armed Bandits

IIT Delhi（印度理工学院德里分校）；IIM Kozhikode（印度管理研究所科泽科德分校）

Sabrina Khurshid, Mohammed Shahid Abdulla, Gourab Ghatak

备注：
Submitted to ACML Journal Track 2024
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AI总结：

本文针对多臂老虎机中夏普比率优化难题，提出正则化平方夏普比率（RSSR）框架，并设计UCB-RSSR及多种最佳臂识别算法，在遗憾最小化和固定预算设置下取得理论保证与实验优势，可应用于风险感知投资组合管理。

摘要：

夏普比率（SR）是刻画金融时间序列的关键参数，因为它通过方差同时考虑了任何股票或投资组合的收益与波动性。推导用于优化SR的在线算法尤其具有挑战性，因为即使是离线策略相对于最佳专家也会产生常数遗憾（Even-Dar等人，2006）。因此，我们不优化通常定义的SR，而是优化正则化平方SR（RSSR）。我们考虑RSSR的两种设置：遗憾最小化（RM）和最佳臂识别（BAI）。在这方面，我们提出了一种新颖的用于RM的多臂老虎机（MAB）算法，称为UCB-RSSR，用于RSSR最大化。我们为RSSR的估计推导了一个路径依赖的集中界。基于此，我们推导了UCB-RSSR的遗憾保证，并证明在双臂老虎机情形下，当进行n个回合时，其遗憾以O(log n)的规模增长。我们还考虑了著名BAI算法（即序列减半和逐次淘汰）的固定预算设置，并提出了SHVV、SHSR和SuRSR算法。我们为所有提出的BAI算法推导了错误概率的上界。我们证明UCB-RSSR优于唯一已知的其他SR优化老虎机算法U-UCB（Cassel等人，2023）。我们还确立了其相对于从GRA-UCB和MVTS算法派生的其他基准的有效性。我们进一步展示了所提出的BAI算法在多种不同设置下的性能。我们的研究强调，我们提出的算法将在风险感知的投资组合管理问题中找到广泛应用。因此，我们的研究强调，我们提出的算法将在风险感知的投资组合管理问题中找到广泛应用。

英文摘要：

Sharpe Ratio (SR) is a critical parameter in characterizing financial time series as it jointly considers the reward and the volatility of any stock/portfolio through its variance. Deriving online algorithms for optimizing the SR is particularly challenging since even offline policies experience constant regret with respect to the best expert Even-Dar et al (2006). Thus, instead of optimizing the usual definition of SR, we optimize regularized square SR (RSSR). We consider two settings for the RSSR, Regret Minimization (RM) and Best Arm Identification (BAI). In this regard, we propose a novel multi-armed bandit (MAB) algorithm for RM called UCB-RSSR for RSSR maximization. We derive a path-dependent concentration bound for the estimate of the RSSR. Based on that, we derive the regret guarantees of UCB-RSSR and show that it evolves as O(log n) for the two-armed bandit case played for a horizon n. We also consider a fixed budget setting for well-known BAI algorithms, i.e., sequential halving and successive rejects, and propose SHVV, SHSR, and SuRSR algorithms. We derive the upper bound for the error probability of all proposed BAI algorithms. We demonstrate that UCB-RSSR outperforms the only other known SR optimizing bandit algorithm, U-UCB Cassel et al (2023). We also establish its efficacy with respect to other benchmarks derived from the GRA-UCB and MVTS algorithms. We further demonstrate the performance of proposed BAI algorithms for multiple different setups. Our research highlights that our proposed algorithms will find extensive applications in risk-aware portfolio management problems. Consequently, our research highlights that our proposed algorithms will find extensive applications in risk-aware portfolio management problems.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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