  The multi-armed bandit (MAB) problem is a ubiquitous decision-making problem
that exemplifies exploration-exploitation tradeoff. Standard formulations
exclude risk in decision making. Risknotably complicates the basic
reward-maximising objectives, in part because there is no universally agreed
definition of it. In this paper, we consider an entropic risk (ER) measure and
explore the performance of a Thompson sampling-based algorithm ERTS under this
risk measure by providing regret bounds for ERTS and corresponding instance
dependent lower bounds.
