Social Learning and Distributed Hypothesis Testing

2016 American Control Conference (ACC)

2016

We propose a new belief update rule for Distributed Non-Bayesian learning in time-varying directed graphs, where a group of agents tries to collectively identify a hypothesis that best describes a sequence of observed data. We show that the proposed update rule, inspired by the Push-Sum algorithm, is consistent; moreover we provide an explicit characterization of its convergence rate. Our main result states that, after a transient time, all agents will concentrate their beliefs at a network independent rate. Network independent rates were not available for other consensus based distributed learning algorithms.

Section: Introductionmentioning

confidence: 99%

“…N00014-12-1-0998. learning structure of the problem [2], [4]. Non-asymptotic rates have been recently derived for fixed graphs [3] and time-varying directed graphs [5].…”

Section: Introductionmentioning

confidence: 99%

Network independent rates in distributed learning

2016 American Control Conference (ACC)

2016

“…In a simultaneous independent effort, the authors in [17], [18] proposed a similar non-Bayesian learning algorithm where a local Bayes update is followed by a consensus step. In [17], convergence result for fixed graphs is provided and large deviation convergence rates are given, proving the existence of a random time after which the beliefs will concentrate exponentially fast. In [18], similar probabilistic bounds for the rate of convergence are derived for fixed graphs and comparisons with the centralized version of the learning rule are provided.…”

mentioning

confidence: 99%

Nonasymptotic convergence rates for cooperative learning over time-varying directed graphs

2015 American Control Conference (ACC)

2015

We study the problem of distributed hypothesis testing with a network of agents where some agents repeatedly gain access to information about the correct hypothesis. The group objective is to globally agree on a joint hypothesis that best describes the observed data at all the nodes. We assume that the agents can interact with their neighbors in an unknown sequence of time-varying directed graphs.Following the pioneering work of Jadbabaie, Molavi, Sandroni, and Tahbaz-Salehi, we propose local learning dynamics which combine Bayesian updates at each node with a local aggregation rule of private agent signals. We show that these learning dynamics drive all agents to the set of hypotheses which best explain the data collected at all nodes as long as the sequence of interconnection graphs is uniformly strongly connected. Our main result establishes a non-asymptotic, explicit, geometric convergence rate for the learning dynamic.

“…In [11], local exponential rates of convergence for undirected gossip-like graphs are studied. The authors in [12], [13] proposed a non-Bayesian learning algorithm where a local Bayes' update is followed by a consensus step. In [12], convergence result for fixed graphs is provided and large deviation convergence rates are given, proving the existence of a random time after which the beliefs will concentrate exponentially fast.…”

Section: Introductionmentioning

confidence: 99%

A tutorial on distributed (non-Bayesian) learning: Problem, algorithms and results

2016 IEEE 55th Conference on Decision and Control (CDC)

2016

Abstract-We overview some results on distributed learning with focus on a family of recently proposed algorithms known as non-Bayesian social learning. We consider different approaches to the distributed learning problem and its algorithmic solutions for the case of finitely many hypotheses. The original centralized problem is discussed at first, and then followed by a generalization to the distributed setting. The results on convergence and convergence rate are presented for both asymptotic and finite time regimes. Various extensions are discussed such as those dealing with directed time-varying networks, Nesterov's acceleration technique and a continuum sets of hypothesis.