Asymptotic Optimality for Decentralised Bandits

• Published in: Dynamic games and applications Vol. 13; no. 1; pp. 307 - 325
• Main Authors: Newton, Conor J., Ganesh, Ayalvadi, Reeve, Henry W. J.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-03-2023; Springer Nature B.V
• Subjects: Agents (artificial intelligence); Algorithms; Artificial intelligence; Asymptotic properties; Communications Engineering; Computer Systems Organization and Communication Networks; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Empirical analysis; Game Theory; Management Science; Mathematics; Mathematics and Statistics; Multi-agent Dynamic Decision Making and Learning; Networks; Operations Research; Optimization; Social and Behav. Sciences
• ISSN: 2153-0785; 2153-0793
• DOI: 10.1007/s13235-022-00451-1

We consider a large number of agents collaborating on a multi-armed bandit problem with a large number of arms. The goal is to minimise the regret of each agent in a communication-constrained setting. We present a decentralised algorithm which builds upon and improves the
Gossip-Insert-Eliminate
method of Chawla et al. (International conference on artificial intelligence and statistics, pp 3471–3481, 2020). We provide a theoretical analysis of the regret incurred which shows that our algorithm is asymptotically optimal. In fact, our regret guarantee matches the asymptotically optimal rate achievable in the full communication setting. Finally, we present empirical results which support our conclusions.