Risk-Constrained Thompson Sampling for CVaR Bandits
This addresses risk-aware decision-making in bandit problems, particularly for applications like finance, but is incremental as it adapts Thompson Sampling to a known risk measure.
The paper tackles the multi-armed bandit problem by incorporating risk via Conditional Value at Risk (CVaR) and proposes a Thompson Sampling-based algorithm, CVaR-TS, which shows improved regret bounds and outperforms existing L/UCB-based algorithms in simulations.
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.