  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.
