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Non-Bayesian Social Learning with Uncertain Models over Time-Varying Directed Graphs
Optimization and Control · Submitted 10 Sep 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that existing non-Bayesian social learning approaches may select a wrong hypothesis with non-zero probability under these conditions.
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The abstract, sentence by sentence
We study the problem of non-Bayesian social learning with uncertain models, in which a network of agents seek to cooperatively identify the state of the world based on a sequence of observed signals. In contrast with the existing literature, we focus our attention on the scenario where the statistical models held by the agents about possible states of the world are built from finite observations. We show that existing non-Bayesian social learning approaches may select a wrong hypothesis with non-zero probability under these conditions. Therefore, we propose a new algorithm to iteratively construct a set of beliefs that indicate whether a certain hypothesis is supported by the empirical evidence. This new algorithm can be implemented over time-varying directed graphs, with non{-}doubly stochastic weights.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the problem of non-Bayesian social learning with uncertain models, in which a network of agents seek to cooperatively identify the state of the world based on a sequence of observed signals. | background 0.84 | 0.48 | 0.04 | asserted 0.90 |
| s1 | In contrast with the existing literature, we focus our attention on the scenario where the statistical models held by the agents about possible states of the world are built from finite observations. | contribution 0.48 | 0.47 | 0.04 | asserted 0.89 |
| s2 | We show that existing non-Bayesian social learning approaches may select a wrong hypothesis with non-zero probability under these conditions. | result 0.53 | 0.57 | 0.27 | hedged possibility 0.84 |
| s3 | Therefore, we propose a new algorithm to iteratively construct a set of beliefs that indicate whether a certain hypothesis is supported by the empirical evidence. | contribution 0.71 | 0.90 | 0.21 | asserted 0.99 |
| s4 | This new algorithm can be implemented over time-varying directed graphs, with non{-}doubly stochastic weights. | method 0.58 | 0.80 | 0.11 | asserted 0.83 |
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The paper
Original abstract
We study the problem of non-Bayesian social learning with uncertain models, in which a network of agents seek to cooperatively identify the state of the world based on a sequence of observed signals. In contrast with the existing literature, we focus our attention on the scenario where the statistical models held by the agents about possible states of the world are built from finite observations. We show that existing non-Bayesian social learning approaches may select a wrong hypothesis with non-zero probability under these conditions. Therefore, we propose a new algorithm to iteratively construct a set of beliefs that indicate whether a certain hypothesis is supported by the empirical evidence. This new algorithm can be implemented over time-varying directed graphs, with non{-}doubly stochastic weights.
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How the literature uses it
2 arXiv papers cite this in 6 sentences
Papers citing it · 2 sentences without a confident label
Compares with it 1 paper
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There, we showed that each false hypothesis $θ$ gets rejected exponentially fast by every agent at the network-independent rate $max_v∈𝒱 K_v(θ^*,θ)$.[In contrast, for linear [ref] and log-linear [ref] rules, the corresponding rate is a convex combination of the relative entropies $K_v(θ^*,θ), v∈𝒱$.] From [ref], we note that under highly sparse communication regimes which correspond to $α< 1$, although learning occurs exponentially fast, the learning rate gets lowered relative to [ref] .
Distributed Inference with Sparse and Quantized Communication · Theoretical Guarantees for Algorithm [ref] · 0.98
Cites it as background 2 papers
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Variations of these learning rules have been proposed to handle fixed and time-varying graphs [ref] , weakly-connected graphs [ref] , increasing self-confidence [ref] , compact hypotheses sets [ref] , and adversarial attacks [ref] .
Non-Bayesian Social Learning with Gaussian Uncertain Models · Introduction · 0.93
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These techniques can be broadly classified in terms of the data aggregation mechanism: while consensus-based linear [ref] and log-linear [ref] rules have been well studied, [ref] and [ref] propose a min-protocol that leads to improved asymptotic learning rates over previous approaches.
Distributed Inference with Sparse and Quantized Communication · Introduction · 0.96
What it cites · 2 sentences without a confident label
Cites as support 1 paper
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This also shows that the transition time for this to occur increases as the number of agents increases, which supports recent theoretical evidence that the network influence is transient in nature [ref] .
Robust Asynchronous Stochastic Gradient-Push: Asymptotically Optimal and Network-Independent Performance for Strongly Convex Functions · Numerical Analysis · 1.00
Cites as background 1 paper
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The solution of problem [ref] has been extensively studied for different graph connectivity assumptions, topologies, observation models, robustness, for which consistency, and both asymptotic and non-asymptotic convergence rates has been established [ref] .
On Increasing Self-Confidence in Non-Bayesian Social Learning over Time-Varying Directed Graphs · Introduction · 0.95
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