Cooperative Bandit Learning in Directed Networks with Arm-Access Constraints

Abstract

Sequential decision-making under uncertainty often involves multiple agents learning which actions (arms) yield the highest rewards through repeated interaction with a stochastic environment. This setting is commonly modeled by cooperative multi-agent multi-armed bandit problems, where agents explore and share information without centralized coordination. In many realistic systems, agents have heterogeneous capabilities that limit their access to subsets of arms and communicate over asymmetric networks represented by directed graphs. In this work, we study multi-agent multi-armed bandit problems with partial arm access, where agents explore and exploit only the arms available to them while exchanging information with neighbors. We propose a distributed consensus-based upper confidence bound (UCB) algorithm that accounts for both the arm accessibility structure and network asymmetry. Our approach employs a mass-preserving information mixing mechanism, ensuring that reward estimates remain unbiased across the network despite accessibility constraints and asymmetric information flow. Under standard stochastic assumptions, we establish logarithmic regret for every agent, with explicit dependence on network mixing properties and arm accessibility constraints. These results quantify how heterogeneous arm access and directed communication shape cooperative learning performance.