  The multi-armed bandit (MAB) problem is a ubiquitous decision-making problem
that exemplifies the exploration-exploitation tradeoff. Standard formulations
exclude risk in decision making. Risk notably complicates the basic
reward-maximising objective, in part because there is no universally agreed
definition of it. In this paper, we consider a popular risk measure in
quantitative finance known as the Conditional Value at Risk (CVaR). We explore
the performance of a Thompson Sampling-based algorithm CVaR-TS under this risk
measure. We provide comprehensive comparisons between our regret bounds with
state-of-the-art L/UCB-based algorithms in comparable settings and demonstrate
their clear improvement in performance. We also include numerical simulations
to empirically verify that CVaR-TS outperforms other L/UCB-based algorithms.
