Non-asymptotic Concentration Rates in Cooperative Learning Part II: Inference on Compact Hypothesis Sets

Cesar A. Uribe, Alexander Olshevsky, Angelia Nedich

Research output: Contribution to journalArticlepeer-review

Abstract

We study the problem of cooperative inference where a group of agents interact over a network and seeks to estimate a joint parameter that best explains a set of network-wide observations using 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 the 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 paper series, we focus on providing a variation approach to distributed Bayesian filtering. Moreover, we develop explicit and computationally efficient algorithms for observation models in the exponential families. Additionally, we provide a novel non-asymptotic belief concentration analysis for distributed non-Bayesian learning on finite hypothesis sets. This new analysis method is the basis for the results presented in Part II. In Part II, we provide the first non-asymptotic belief concentration rate analysis for distributed non-Bayesian learning over networks on compact hyp

Original languageEnglish (US)
JournalIEEE Transactions on Control of Network Systems
DOIs
StateAccepted/In press - 2022

Keywords

  • Bayes methods
  • Computational modeling
  • Distributed Inference
  • estimation over networks
  • Maximum likelihood estimation
  • Network topology
  • non-asymptotic rates
  • non-Bayesian social learning
  • Numerical models
  • Random variables
  • Task analysis

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Control and Optimization

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