Thompson Sampling for Combinatorial Semi-Bandits - Wang, Siwei; Chen, Wei (Proceedings of the 35th International Conference on Machine Learning (ICML'2018), 2018)
We study the application of the Thompson sampling (TS) methodology to the stochastic combinatorial multi-armed bandit (CMAB) framework. We analyze the standard TS algorithm for the general CMAB, and obtain the first distribution-dependent regret bound of for TS under general CMAB, where m is the number of arms, T is the time horizon, and is the minimum gap between the expected reward of the optimal solution and any non-optimal solution. We also show that one cannot use an approximate oracle in TS algorithm for even MAB problems. Then we expand the analysis to matroid bandit, a special case of CMAB and for which we could remove the independence assumption across arms and achieve a better regret bound. Finally, we use some experiments to show the comparison of regrets of CUCB and CTS algorithms.