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

Learning to Route Orders with Risk in Mind How should a trader split an order across multiple venues when both returns and risk matter? In “Risk-Aware Linear Bandits: Theory and Applications in Smart Order Routing,” Jingwei Ji, Renyuan Xu, and Ruihao Zhu develop a new bandit framework for this problem by combining mean variance optimization with linear bandit structure. Their model is motivated by smart order routing, where traders must learn from partial feedback while facing a very large action space. The authors propose two algorithms, RISE and RISE++, and show that both achieve near-optimal regret guarantees while avoiding the strong dependence on the number of actions that limits existing risk-aware bandit methods. They also validate the linear approximation empirically using the NASDAQ ITCH data set and demonstrate strong numerical performance in both synthetic and market-based experiments. The paper opens a new path for risk-sensitive online learning in financial decision making.