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 arm, and decision maker chooses one arm to pull receives corresponding reward. particular, mean-variance as risk criterion, best is with largest We apply Thompson sampling algorithm disjoint model, provide comprehensive regret analysis variant of proposed algorithm. For T rounds, K actions, d-dimensional feature vectors, prove bound $$O\left({\left({1 + \rho {1 \over \rho}} \right)d\,\ln \,T\ln {K \delta}\sqrt {dK{T^{1 2}}\ln \delta}{1 \over}}} \right)$$ that holds probability 1 − δ criterion tolerance ρ, any $$0 < \in \frac{1}{2},0 \delta 1$$ . The empirical performance our algorithms demonstrated via portfolio selection problem.