Thompson Sampling Algorithms for Cascading Bandits

TL;DR

This paper provides the first theoretical analysis of Thompson Sampling algorithms for cascading bandits, offering tighter regret bounds, new algorithm designs, and empirical evidence of superior performance over UCB methods.

Contribution

It introduces and analyzes Thompson Sampling algorithms for cascading bandits, including a Gaussian update variant and a linear generalization, with proven regret bounds and empirical validation.

Findings

TS algorithms outperform UCB algorithms in experiments.

New regret bounds are tighter than previous results.

Linear TS algorithm scales efficiently with model dimension.

Abstract

Motivated by the pressing need for efficient optimization in online recommender systems, we revisit the cascading bandit model proposed by Kveton et al. (2015). While Thompson sampling (TS) algorithms have been shown to be empirically superior to Upper Confidence Bound (UCB) algorithms for cascading bandits, theoretical guarantees are only known for the latter. In this paper, we first provide a problem-dependent upper bound on the regret of a TS algorithm with Beta-Bernoulli updates; this upper bound is tighter than a recent derivation under a more general setting by Huyuk and Tekin (2019). Next, we design and analyze another TS algorithm with Gaussian updates, TS-Cascade. TS-Cascade achieves the state-of-the-art regret bound for cascading bandits. Complementarily, we consider a linear generalization of the cascading bandit model, which allows efficient learning in large cascading bandit problem instances. We introduce and analyze a TS algorithm, which enjoys a regret bound that depends on the dimension of the linear model but not the number of items. Finally, by using information-theoretic techniques and judiciously constructing cascading bandit instances, we derive a nearly matching regret lower bound for the standard model. Our paper establishes the first theoretical guarantees on TS algorithms for stochastic combinatorial bandit problem model with partial feedback. Numerical experiments demonstrate the superiority of the proposed TS algorithms compared to existing UCB-based ones.