English

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

Machine Learning 2022-10-13 v2 Machine Learning

Abstract

We propose the first regret-based approach to the Graphical Bilinear Bandits problem, where nn 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 O~(T)\tilde{O}(\sqrt{T}) on the α\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.

Keywords

Cite

@article{arxiv.2206.00466,
  title  = {An $\alpha$-No-Regret Algorithm For Graphical Bilinear Bandits},
  author = {Geovani Rizk and Igor Colin and Albert Thomas and Rida Laraki and Yann Chevaleyre},
  journal= {arXiv preprint arXiv:2206.00466},
  year   = {2022}
}
R2 v1 2026-06-24T11:35:55.560Z