Joel Q. L. Chang

Joel Q. L. Chang, Vincent Y. F. Tan

This paper unifies the design and the analysis of risk-averse Thompson sampling algorithms for the multi-armed bandit problem for a class of risk functionals $ρ$ that are continuous and dominant. We prove generalised concentration bounds for these continuous and dominant risk functionals and show that a wide class of popular risk functionals belong to this class. Using our newly developed analytical toolkits, we analyse the algorithm $ρ$-MTS (for multinomial distributions) and prove that they admit asymptotically optimal regret bounds of risk-averse algorithms under CVaR, proportional hazard, and other ubiquitous risk measures. More generally, we prove the asymptotic optimality of $ρ$-MTS for Bernoulli distributions for a class of risk measures known as empirical distribution performance measures (EDPMs); this includes the well-known mean-variance. Numerical simulations show that the regret bounds incurred by our algorithms are reasonably tight vis-à-vis algorithm-independent lower bounds.

Ming Liang Ang, Eloise Y. Y. Lim, Joel Q. L. Chang

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.

Joel Q. L. Chang, Qiuyu Zhu, Vincent Y. F. Tan

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.