Thompson Sampling for Combinatorial Semi-bandits with Sleeping Arms and Long-Term Fairness Constraints

We study the combinatorial sleeping multi-armed semi-bandit problem with long-term fairness constraints~(CSMAB-F). To address the problem, we adopt Thompson Sampling~(TS) to maximize the total rewards and use virtual queue techniques to handle the fairness constraints, and design an algorithm called TS with beta priors and Bernoulli likelihoods for CSMAB-F~(TSCSF-B). Further, we prove TSCSF-B can satisfy the fairness constraints, and the time-averaged regret is upper bounded by fracN2η + Oleft(frac√mNTln TTright), where N is the total number of arms, m is the maximum number of arms that can be pulled simultaneously in each round~(the cardinality constraint) and η is the parameter trading off fairness for rewards. By relaxing the fairness constraints (i.e., let η rightarrow ∞), the bound boils down to the first problem-independent bound of TS algorithms for combinatorial sleeping multi-armed semi-bandit problems. Finally, we perform numerical experiments and use a high-rating movie recommendation application to show the effectiveness and efficiency of the proposed algorithm.