Distributed Bandits: Probabilistic Communication on d-regular Graphs

We study the decentralized multi-agent multi-armed bandit problem for agents that communicate with probability over a network defined by a d-regular graph. Every edge in the graph has probabilistic weight p to account for the (1 - p) probability of a communication link failure. At each time step, each agent chooses an arm and receives a numerical reward associated with the chosen arm. After each choice, each agent observes the last obtained reward of each of its neighbors with probability p. We propose a new Upper Confidence Bound (UCB) based algorithm and analyze how agent-based strategies contribute to minimizing group regret in this probabilistic communication setting. We provide theoretical guarantees that our algorithm outperforms state-of-the-art algorithms. We illustrate our results and validate the theoretical claims using numerical simulations.