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 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 on the -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.
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}
}