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The multi-armed bandit (MAB) problem is a ubiquitous decision-making problemthat exemplifies exploration-exploitation tradeoff. Standard formulationsexclude risk in decision making. Risknotably complicates the basicreward-maximising objectives, in part because there is no universally agreeddefinition of it. In this paper, we consider an entropic risk (ER) measure andexplore the performance of a Thompson sampling-based algorithm ERTS under thisrisk measure by providing regret bounds for ERTS and corresponding instancedependent lower bounds.

Thompson Sampling for Gaussian Entropic Risk Bandits