Nonasymptotic Concentration Rates in Cooperative Learning-Part I: Variational Non-Bayesian Social Learning

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...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on control of network systems Vol. 9; no. 3; pp. 1128 - 1140
Main Authors: Uribe, Cesar A., Olshevsky, Alexander, Nedic, Angelia
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.09.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Bayes methods
Bayesian analysis
Computational modeling
Cooperative learning
Distributed inference
estimation over networks
Hypotheses
Inference
Machine learning
Mathematical models
Maximum likelihood estimation
Mirrors
Network topologies
non-Bayesian social learning
nonasymptotic rates
Numerical analysis
Optimization
Parameters
Probability distribution functions
Random variables
Stochastic processes
ISSN:2325-5870, 2372-2533
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2325-5870
2372-2533
DOI:10.1109/TCNS.2022.3140683