Multi-Agent Best Arm Identification in Stochastic Linear Bandits

We study the problem of collaborative best-arm identification in stochastic linear bandits under a fixed-budget scenario. In our learning model, we consider multiple agents connected through a star network or a generic network, interacting with a linear bandit instance in parallel. The objective of the agents is to collaboratively learn the best arm of the given bandit instance with the help of a central server while minimizing the probability of error in best arm estimation. For this purpose, we devise the algorithms MaLinBAI-Star and MaLinBAI-Gen for star networks and generic networks respectively. Both algorithms employ an Upper-Confidence-Bound approach where agents share their knowledge through the central server during each communication round. We demonstrate, both theoretically and empirically, that our algorithms enjoy exponentially decaying probability of error in the allocated time budget. Furthermore, experimental results based on synthetic and real-world data validate the effectiveness of our algorithms over the existing multi-agent algorithms.