Collaborative Contextual Combinatorial Cascading Thompson Sampling

Abstract

We design and analyze collaborative contextual combinatorial cascading Thompson sampling ($C^4$-TS). $C^4$-TS is a Bayesian heuristic to address the cascading bandit problem in the collaborative environment. $C^4$-TS utilizes posterior sampling strategy to balance the exploration-exploitation tradeoff and it also incorporates the collaborative effect to share information across similar users. Utilizing these two novel features, we prove that the regret upper bound for $C^4$-TS is $\tilde{O}(d (u+\sqrt{mKT}))$, where d is the dimension of the feature space, u is the number of users, m is the number of clusters, K is the length of the recommended list and T is the time horizon. This regret upper bound matches the theoretical guarantee for UCB-like algorithm in the same settings. We also conduct a set of simulations comparing $C^4$-TS with the state-of-the-art algorithms. The empirical results demonstrate the advantage of our algorithm over existing works.