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

arXiv: https://arxiv.org/abs/2208.02389 · HTML: https://mlsanity.com/paper/2208.02389/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 53 references that are in the map.
- First posted on arXiv 4 Aug 2022.

## Builds on (most cited first, 14 of 14)

- [Reinforcement Learning in Healthcare: A Survey](https://mlsanity.com/paper/1908.08796/) (2019)
- [Recent Advances in Reinforcement Learning in Finance](https://mlsanity.com/paper/2112.04553/) (2021)
- [MNL-Bandit: A Dynamic Learning Approach to Assortment Selection](https://mlsanity.com/paper/1706.03880/) (2017)
- [Hedging the Drift: Learning to Optimize under Non-Stationarity](https://mlsanity.com/paper/1903.01461/) (2019)
- [Thompson Sampling Algorithms for Mean-Variance Bandits](https://mlsanity.com/paper/2002.00232/) (2020)
- [Robustness Implies Generalization via Data-Dependent Generalization Bounds](https://mlsanity.com/paper/2206.13497/) (2022)
- [Reinforcement Learning with Dynamic Convex Risk Measures](https://mlsanity.com/paper/2112.13414/) (2021)
- [Risk-Averse Multi-Armed Bandit Problems under Mean-Variance Measure](https://mlsanity.com/paper/1604.05257/) (2016)
- [Distributionally Robust Batch Contextual Bandits](https://mlsanity.com/paper/2006.05630/) (2020)
- [No Weighted-Regret Learning in Adversarial Bandits with Delays](https://mlsanity.com/paper/2103.04550/) (2021)
- [Delay-Adaptive Learning in Generalized Linear Contextual Bandits](https://mlsanity.com/paper/2003.05174/) (2020)
- [A Survey of Risk-Aware Multi-Armed Bandits](https://mlsanity.com/paper/2205.05843/) (2022)
- [Robo-advising: Learning Investors' Risk Preferences via Portfolio Choices](https://mlsanity.com/paper/1911.02067/) (2019)
- [Safe Data Collection for Offline and Online Policy Learning](https://mlsanity.com/paper/2111.04835/) (2021)

## Built on by (most cited first, 1 of 1)

- [Stochastic Linear Bandits with Parameter Noise](https://mlsanity.com/paper/2601.23164/) (2026)

## Abstract (arXiv)

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 ITCH dataset, we initiate the study of risk-aware linear bandits. In this setting, we aim at minimizing regret, which measures our performance deficit compared to 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 (G-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 rigorously analyze their near-optimal regret upper bounds to show that, by leveraging the linear structure, our algorithms can dramatically reduce the regret when compared to 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 dataset. Our results reveal that 1) The linear structure assumption can indeed be well supported by the Nasdaq dataset; and more importantly 2) Both RISE and RISE++ can significantly outperform the competing methods, in terms of regret, especially in complex decision-making scenarios.