Thompson Sampling Algorithms for Mean-Variance Bandits
This addresses risk-aware decision-making in online systems, offering a novel approach with improved performance over prior work.
The authors tackled the problem of incorporating risk into multi-armed bandits by developing Thompson Sampling algorithms for mean-variance optimization, achieving the best known regret bounds and outperforming existing methods in simulations.
The multi-armed bandit (MAB) problem is a classical learning task that exemplifies the exploration-exploitation tradeoff. However, standard formulations do not take into account {\em risk}. In online decision making systems, risk is a primary concern. In this regard, the mean-variance risk measure is one of the most common objective functions. Existing algorithms for mean-variance optimization in the context of MAB problems have unrealistic assumptions on the reward distributions. We develop Thompson Sampling-style algorithms for mean-variance MAB and provide comprehensive regret analyses for Gaussian and Bernoulli bandits with fewer assumptions. Our algorithms achieve the best known regret bounds for mean-variance MABs and also attain the information-theoretic bounds in some parameter regimes. Empirical simulations show that our algorithms significantly outperform existing LCB-based algorithms for all risk tolerances.