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We consider a K-armed bandit problem in general graphs where agents arearbitrarily connected and each of them has limited memorizing capabilities andcommunication bandwidth. The goal is to let each of the agents eventually learnthe best arm. It is assumed in these studies that the communication graphshould be complete or well-structured, whereas such an assumption is not alwaysvalid in practice. Furthermore, limited memorization and communicationbandwidth also restrict the collaborations of the agents, since the agentsmemorize and communicate very few experiences. Additionally, an agent may becorrupted to share falsified experiences to its peers, while the resource limitin terms of memorization and communication may considerably restrict thereliability of the learning process. To address the above issues, we propose athree-staged collaborative learning algorithm. In each step, the agents sharetheir latest experiences with each other through light-weight random walks in ageneral communication graph, and then make decisions on which arms to pullaccording to the recommendations received from their peers. The agents finallyupdate their adoptions (i.e., preferences to the arms) based on the rewardobtained by pulling the arms. Our theoretical analysis shows that, when thereare a sufficient number of agents participating in the collaborative learningprocess, all the agents eventually learn the best arm with high probability,even with limited memorizing capabilities and light-weight communications. Wealso reveal in our theoretical analysis the upper bound on the number ofcorrupted agents our algorithm can tolerate. The efficacy of our proposedthree-staged collaborative learning algorithm is finally verified by extensiveexperiments on both synthetic and real datasets.

Collaborative Learning in General Graphs with Limited Memorization: Complexity, Learnability, and Reliability