Risk-averse Contextual Multi-armed Bandit Problem with Linear Payoffs

In this paper we consider the contextual multi-armed bandit problem for linear payoffs under a risk-averse criterion. At each round, contexts are revealed for each arm, and the decision maker chooses one arm to pull and receives the corresponding reward. In particular, we consider mean-variance as the risk criterion, and the best arm is the one with the largest mean-variance reward. We apply the Thompson sampling algorithm for the disjoint model, and provide a comprehensive regret analysis for a variant of the proposed algorithm. For T rounds, K actions, and d-dimensional feature vectors, we prove a regret bound of O((1 + rho + 1/rho)d ln T ln K/delta root dKT(1+2 epsilon) ln K/delta 1/epsilon) that holds with probability 1 - delta under the mean-variance criterion with risk tolerance rho, for any 0 < epsilon < 1/2, 0 < delta < 1. The empirical performance of our proposed algorithms is demonstrated via a portfolio selection problem.