On Increasing Self-Confidence in Non-Bayesian Social Learning over Time-Varying Directed Graphs

Uribe, César A.; Jadbabaie, Ali

doi:10.23919/acc.2019.8815382

Cited by 9 publications

(4 citation statements)

References 21 publications

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“…Then, the beliefs are updated by scaling the combined beliefs by the likelihood of their new observation given that the particular model is the ground truth. Variations of these learning rules have been proposed to handle fixed and time-varying graphs [11], weakly-connected graphs [12], [13], increasing self-confidence [14], compact hypotheses sets [15], and adversarial attacks [16], [17].…”

Section: Introductionmentioning

confidence: 99%

Non-Bayesian Social Learning with Gaussian Uncertain Models

Hare

Uribe

Kaplan

et al. 2020

2020 American Control Conference (ACC)

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Non-Bayesian social learning theory provides a framework for distributed inference of a group of agents interacting over a social network by sequentially communicating and updating beliefs about the unknown state of the world through likelihood updates from their observations. Typically, likelihood models are assumed known precisely. However, in many situations the models are generated from sparse training data due to lack of data availability, high cost of collection/calibration, limits within the communications network, and/or the high dynamics of the operational environment. Recently, social learning theory was extended to handle those model uncertainties for categorical models. In this paper, we introduce the theory of Gaussian uncertain models and study the properties of the beliefs generated by the network of agents. We show that even with finite amounts of training data, non-Bayesian social learning can be achieved and all agents in the network will converge to a consensus belief that provably identifies the best estimate for the state of the world given the set of prior information.This research was sponsored by the DARPA Lagrange, Vannevar Bush Fellowship, and OSD LUCI programs.J.Z.H. and L.K.

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Section: Introductionmentioning

confidence: 99%

Non-Bayesian Social Learning with Gaussian Uncertain Models

Hare

Uribe

Kaplan

et al. 2020

2020 American Control Conference (ACC)

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“…Then, using property (a) of Proposition III.1, the posterior distribution converges in probability to a delta function as 𝑡 → ∞, i.e., lim 𝑡→∞ 𝑓 (𝜑|𝜓(𝜔 1:𝑡 )) = 𝛿 𝜑 𝜃 * (𝜑). This results in (17) converging in probability to…”

Section: Asymptotic Properties Of the Uncertain Likelihood Ratiomentioning

confidence: 99%

“…Several social learning (fusion) rules have been proposed in the literature, including weighted averages [1], [6], geometric averages [7]- [9], constant elasticity of substitution models [10], and minimum operators [11], [12]. These learning rules have been applied to undirected/directed graphs, timevarying graphs [13], [14], weakly-connected graphs [15], [16], agents with increasing self-confidence [17], compact hypothesis sets [18], and under adversarial attacks [19]- [22]. Each approach presents a variation of one of the above learning rules and provides theoretical guarantees (asymptotically) that the agents will learn the true state of the world.…”

Section: Introductionmentioning

confidence: 99%

A General Framework for Distributed Inference with Uncertain Models

Hare¹,

Uribe²,

Kaplan³

et al. 2020

Preprint

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This paper studies the problem of distributed classification with a network of heterogeneous agents. The agents seek to jointly identify the underlying target class that best describes a sequence of observations. The problem is first abstracted to a hypothesis-testing framework, where we assume that the agents seek to agree on the hypothesis (target class) that best matches the distribution of observations. Non-Bayesian social learning theory provides a framework that solves this problem in an efficient manner by allowing the agents to sequentially communicate and update their beliefs for each hypothesis over the network. Most existing approaches assume that agents have access to exact statistical models for each hypothesis. However, in many practical applications, agents learn the likelihood models based on limited data, which induces uncertainty in the likelihood function parameters. In this work, we build upon the concept of uncertain models to incorporate the agents' uncertainty in the likelihoods by identifying a broad set of parametric distribution that allows the agents' beliefs to converge to the same result as a centralized approach. Furthermore, we empirically explore extensions to non-parametric models to provide a generalized framework of uncertain models in non-Bayesian social learning.This research was sponsored by the DARPA Lagrange, Vannevar Bush Fellowship, and OSD LUCI programs.J.Z.H. and L.K.

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“…C. A. Uribe is with the Laboratory for Information and Decision Systems -LIDS, Massachusetts Institute of Technology -M.I.T., Cambridge, MA, USA. E-mails: eamojican@unal.edu.co, dryanguasr@unal.edu.co, cauribe@mit.edu, rules have been applied to undirected/directed graphs, timevarying graphs [14], [15], weakly-connected graphs [16], agents with increasing self-confidence [17], compact hypothesis sets [18], uncertain models [19], and under adversarial attacks [20]- [23].…”

Section: Introductionmentioning

confidence: 99%

Robust Asynchronous and Network-Independent Cooperative Learning

Mojica‐Nava¹,

Yanguas-Rojas²,

Uribe³

2020

Preprint

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We consider the model of cooperative learning via distributed non-Bayesian learning, where a network of agents tries to jointly agree on a hypothesis that best described a sequence of locally available observations. Building upon recently proposed weak communication network models, we propose a robust cooperative learning rule that allows asynchronous communications, message delays, unpredictable message losses, and directed communication among nodes. We show that our proposed learning dynamics guarantee that all agents in the network will have an asymptotic exponential decay of their beliefs on the wrong hypothesis, indicating that the beliefs of all agents will concentrate on the optimal hypotheses. Numerical experiments provide evidence on a number of network setups.

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On Increasing Self-Confidence in Non-Bayesian Social Learning over Time-Varying Directed Graphs

Cited by 9 publications

References 21 publications

Non-Bayesian Social Learning with Gaussian Uncertain Models

Non-Bayesian Social Learning with Gaussian Uncertain Models

A General Framework for Distributed Inference with Uncertain Models

Robust Asynchronous and Network-Independent Cooperative Learning

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