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Non-Bayesian Social Learning with Observation Reuse and Soft Switching

机译：具有观察重用和软切换的非贝叶斯社会学习

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摘要

We propose a non-Bayesian social learning update rule for agents in a network, which minimizes the sum of the Kullback-Leibler divergence between the true distribution generating the agents' local observations and the agents' beliefs (parameterized by a hypothesis set), and a weighted varentropy-related term. The varentropy-related term allows us to control the rate of convergence of our update rule, which also reuses some of the most recent observations of each agent to speed up convergence. Under mild technical conditions, we show that the belief of each agent concentrates on the optimal hypothesis set, and we derive a bound for the convergence rate. Furthermore, to overcome the performance degradation due to misinforming agents, who use a corrupted likelihood functions in their belief updates, we propose to use multiple social networks that update their beliefs independently and a convex combination mechanism among the beliefs of all the networks. Simulations with applications to location identification and group recommendation demonstrate that our proposed methods offer improvements over two other current state-of-the art non-Bayesian social learning algorithms.
机译：我们为网络中的代理人提出了一个非贝叶斯社会学习更新规则，该规则将生成代理人的本地观察结果的真实分布与代理人的信念（由假设集进行参数化）之间的Kullback-Leibler差异之和最小化，并且与变态熵相关的加权项。与变熵相关的术语使我们能够控制更新规则的收敛速度，该规则还重用了每个代理的最新观察结果以加快收敛速度​​。在温和的技术条件下，我们证明了每个代理的信念都集中在最优假设集上，并且得出了收敛速度的界线。此外，为了克服由于错误通知的代理（在他们的信念更新中使用损坏的似然函数）导致的性能下降，我们建议使用独立更新其信念的多个社交网络以及所有网络的信念之间的凸组合机制。通过对位置识别和组推荐的应用进行的仿真表明，我们提出的方法相对于其他两种当前的最新非贝叶斯社交学习算法提供了改进。

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