On Regret-optimal Cooperative Nonstochastic Multi-armed Bandits
This addresses the challenge of distributed decision-making under uncertainty for networked agents, representing an incremental theoretical advance in multi-agent bandit algorithms.
The paper tackles the problem of cooperative multi-agent multi-armed bandits with communication delays, showing a lower bound for individual regret and developing a collaborative FTRL algorithm that matches this bound up to a constant factor under certain conditions.
We consider the nonstochastic multi-agent multi-armed bandit problem with agents collaborating via a communication network with delays. We show a lower bound for individual regret of all agents. We show that with suitable regularizers and communication protocols, a collaborative multi-agent \emph{follow-the-regularized-leader} (FTRL) algorithm has an individual regret upper bound that matches the lower bound up to a constant factor when the number of arms is large enough relative to degrees of agents in the communication graph. We also show that an FTRL algorithm with a suitable regularizer is regret optimal with respect to the scaling with the edge-delay parameter. We present numerical experiments validating our theoretical results and demonstrate cases when our algorithms outperform previously proposed algorithms.