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

TL;DR

This paper introduces TSCSF-B, a Thompson Sampling-based algorithm for combinatorial sleeping semi-bandits with long-term fairness constraints, providing theoretical guarantees and demonstrating effectiveness in a movie recommendation application.

Contribution

The paper develops TSCSF-B, a novel Thompson Sampling algorithm that handles fairness constraints in combinatorial sleeping semi-bandits, with proven regret bounds and practical validation.

Findings

TSCSF-B satisfies fairness constraints.

Regret bound is tight and problem-independent when fairness is relaxed.

Numerical experiments confirm effectiveness in recommendation systems.

Abstract

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 \emph{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 $\frac{N}{2\eta} + O\left(\frac{\sqrt{mNT\ln T}}{T}\right)$, 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 $\eta$ is the parameter trading off fairness for rewards. By relaxing the fairness constraints (i.e., let $\eta \rightarrow \infty$), 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.