Cooperative Multi-Agent Graph Bandits: UCB Algorithm and Regret Analysis
This addresses the problem of efficient exploration in cooperative multi-agent systems on graphs for researchers in reinforcement learning and bandit theory, but it is incremental as it builds directly on prior single-agent work.
The paper tackles the multi-agent graph bandit problem by extending a single-agent formulation to cooperative agents, proposing the Multi-G-UCB algorithm and proving an expected regret bound of O(γN log(T)[√(KT) + DK]).
In this paper, we formulate the multi-agent graph bandit problem as a multi-agent extension of the graph bandit problem introduced by Zhang, Johansson, and Li [CISS 57, 1-6 (2023)]. In our formulation, $N$ cooperative agents travel on a connected graph $G$ with $K$ nodes. Upon arrival at each node, agents observe a random reward drawn from a node-dependent probability distribution. The reward of the system is modeled as a weighted sum of the rewards the agents observe, where the weights capture some transformation of the reward associated with multiple agents sampling the same node at the same time. We propose an Upper Confidence Bound (UCB)-based learning algorithm, Multi-G-UCB, and prove that its expected regret over $T$ steps is bounded by $O(γN\log(T)[\sqrt{KT} + DK])$, where $D$ is the diameter of graph $G$ and $γ$ a boundedness parameter associated with the weight functions. Lastly, we numerically test our algorithm by comparing it to alternative methods.