  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.
