In this paper we study the problem of social learning under multiple true hypotheses and self-interested agents which exchange information over a graph. In this setup, each agent receives data that might be generated from a different hypothesis (or state) than the data other agents receive. In contrast to the related literature in social learning, which focuses on showing that the network achieves consensus, here we study the case where every agent is self-interested and wants to find the hypothesis that generates its own observations. However, agents do not know which ones of their peers wants to find the same state with them and as a result they do not know which agents they should cooperate with. To this end, we propose a scheme with adaptive combination weights and study the consistency of the agents' learning process. The scheme allows each agent to identify and collaborate with neighbors that observe the same hypothesis, while excluding others, thus resulting in improved performance compared to both non-cooperative learning and cooperative social learning solutions. We analyze the asymptotic behavior of agents' beliefs under the proposed social learning algorithm and provide sufficient conditions that enable all agents to correctly identify their true hypotheses. The theoretical analysis is corroborated by numerical simulations.
翻译:在本文中,我们研究了在多个真实假设和以图表交换信息的自我感兴趣的代理人下进行社会学习的问题。在这个设置中,每个代理人接收的数据可能来自与其他代理人收到的数据不同的假设(或状态),而社会学习的相关文献侧重于显示网络能够达成共识,我们在此研究每个代理人都是自我感兴趣的案例,希望找到产生自己观察结果的假设。然而,代理人不知道他们的同龄人希望与他们找到同样的状态,因此不知道他们应该与哪个代理人合作。为此,我们提出了一个具有适应性组合权重和研究代理人学习过程一致性的计划。这个计划允许每个代理人与遵守同一假设的邻居进行识别与合作,同时排除其他人,从而与不合作性学习和合作性社会学习解决方案相比,提高了业绩。我们分析了在拟议的社会学习算法下代理人信仰的无谓行为,并提供了充分的条件,使所有代理人能够正确识别其真实的假说。理论分析得到数字模拟的证实。