Risk-Aware Linear Bandits: Theory and Applications in Smart Order Routing

• 成果类型: Article; Early Access
• 署名作者: Ji, Jingwei; Xu, Renyuan; Zhu, Ruihao
• 署名单位: Stanford University; Cornell University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2024.0771
• 发表日期: 2026-05-15
• 关键词: Online learning; risk-aware bandits; Regret Analysis; smart order routing; Algorithmic trading; mean variance; PORTFOLIO SELECTION; MODEL

摘要

Motivated by practical considerations in machine learning for financial decision making, such as risk aversion and large action space, we consider risk-aware bandits optimization with applications in smart order routing (SOR). Specifically, based on preliminary observations of linear price impacts made from the Nasdaq TotalView-ITCH (NASDAQ ITCH) data set, we initiate the study of risk-aware linear bandits. In this setting, we aim at minimizing regret, which measures our performance deficit compared with the optimum's, under the mean variance metric when facing a set of actions whose rewards are linear functions of (initially) unknown parameters. Driven by the variance-minimizing globally optimal design, we propose the novel instance-independent risk-aware explore-then-commit (RISE) algorithm and the instance-dependent risk-aware successive elimination (RISE++) algorithm. Then, we analyze their near-optimal regret upper bounds to show that, by leveraging the linear structure, our algorithms can dramatically reduce the regret when compared with existing methods. Finally, we demonstrate the performance of the algorithms by conducting extensive numerical experiments in the SOR setup using both synthetic datasets and the NASDAQ ITCH data set. Our results reveal that (1) the linear structure assumption can indeed be well supported by the NASDAQ data set, and more importantly, (2) both RISE and RISE++ can significantly outperform the competing methods, in terms of mean variance regret, especially in complex decision-making scenarios.