An $\alpha$-No-Regret Algorithm For Graphical Bilinear Bandits

TL;DR

This paper introduces the first regret-based algorithm for graphical bilinear bandits, addressing a complex NP-hard problem by leveraging optimism in the face of uncertainty, with theoretical guarantees and experimental validation.

Contribution

It presents a novel regret-based algorithm for graphical bilinear bandits, filling a gap in the literature and analyzing the impact of graph structure on convergence.

Findings

Achieves an upper bound of (\,T) on -regret.

Demonstrates the algorithm's effectiveness through experiments.

Shows the influence of graph structure on convergence rate.

Abstract

We propose the first regret-based approach to the Graphical Bilinear Bandits problem, where $n$ agents in a graph play a stochastic bilinear bandit game with each of their neighbors. This setting reveals a combinatorial NP-hard problem that prevents the use of any existing regret-based algorithm in the (bi-)linear bandit literature. In this paper, we fill this gap and present the first regret-based algorithm for graphical bilinear bandits using the principle of optimism in the face of uncertainty. Theoretical analysis of this new method yields an upper bound of $\tilde{O}(\sqrt{T})$ on the $\alpha$-regret and evidences the impact of the graph structure on the rate of convergence. Finally, we show through various experiments the validity of our approach.