Nonasymptotic Concentration Rates in Cooperative Learning–Part I: Variational Non-Bayesian Social Learning
Nonasymptotic Concentration Rates in Cooperative Learning–Part I: Variational Non-Bayesian Social Learning
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DOI：
10.1109/tcns.2022.3140683
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发表时间：
2022-09
影响因子：
4.2
通讯作者：
César A. Uribe;Alexander Olshevsky;A. Nedich
中科院分区：
文献类型：
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作者：
César A. Uribe;Alexander Olshevsky;A. Nedich
在这篇文章中，我们研究了合作推理的问题，其中一组代理在网络上进行交互，并试图估计一个联合参数，最好地解释了一组网络范围内的observationsusing本地信息。代理不知道网络拓扑或其他代理的观察结果。我们探讨了变分解释的贝叶斯后验及其关系的随机镜像下降算法证明，在适当的假设下，所提出的算法产生的信念集中在真正的参数指数快速。在这个由两部分组成的系列文章的第一部分中，我们重点介绍了分布式贝叶斯过滤的变分方法。此外，我们开发了计算效率的算法在指数族的观测模型。我们提供了一种新的非渐近信念集中分析的分布式非贝叶斯学习有限假设集。这一新的分析是第二部分所列结果的基础。在第二部分中，我们提供了第一个非渐近信念集中率分析，用于网络上的分布式非贝叶斯学习。此外，我们提供了广泛的数值分析的各种分布式推理任务在网络上的指数分布族的观测模型。
In this article, we studied the problem of cooperative inference where a group of agents interacts over a network and seeks to estimate a joint parameter that best explains a set of network-wide observationsusing local information only. Agents do not know the network topology or the observations of other agents. We explore a variational interpretation of the Bayesian posterior and its relation to stochastic mirror descent algorithm to prove that, under appropriate assumptions, the beliefs generated by the proposed algorithm concentrate around the true parameter exponentially fast. In part I of this two-part article series, we focus on providing a variational approach to distributed Bayesian filtering. Moreover, we develop computationally efficient algorithms for observation models in exponential families. We provide a novel nonasymptotic belief concentration analysis for distributednon-Bayesian learning on finite hypothesis sets. This new analysis is the basis for the results presented in Part II. We provide the first nonasymptotic belief concentration rate analysis for distributed non-Bayesian learning over networks on compact hypothesis sets in Part II. In addition, we provide extensive numerical analysis for various distributed inference tasks on networks for observational models in the exponential distribution families.