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Non-Bayesian Social Learning with Multiview Observations

Dongyan Sui, Weichen Cao, Stefan Vlaski, Chun Guan, Siyang Leng

TL;DR

This work extends non-Bayesian social learning to settings with multiview observations by allowing independent Bayesian updates per signal type and a cross-view information-aggregation step across a directed network. By introducing signal-type weights $\gamma_l$ and constructing an augmented interaction matrix $\tilde{A}$, the authors prove almost-sure convergence to the true state under standard assumptions, and derive a mislearning-robustness condition that accommodates misleading signals. Theoretical results are complemented by numerical experiments in distributed localization tasks, demonstrating that integrating multiple viewpoints resolves observational ambiguities and enhances fault tolerance. The framework broadens the applicability of distributed inference to multi-feature environments and motivates future work on applying multiview social learning to high-dimensional, real-world sensor networks and multi-agent systems.

Abstract

Non-Bayesian social learning enables multiple agents to conduct networked signal and information processing through observing environmental signals and information aggregating. Traditional non-Bayesian social learning models only consider single signals, limiting their applications in scenarios where multiple viewpoints of information are available. In this work, we exploit, in the information aggregation step, the independently learned results from observations taken from multiple viewpoints and propose a novel non-Bayesian social learning model for scenarios with multiview observations. We prove the convergence of the model under traditional assumptions and provide convergence conditions for the algorithm in the presence of misleading signals. Through theoretical analyses and numerical experiments, we validate the strong reliability and robustness of the proposed algorithm, showcasing its potential for real-world applications.

Non-Bayesian Social Learning with Multiview Observations

TL;DR

This work extends non-Bayesian social learning to settings with multiview observations by allowing independent Bayesian updates per signal type and a cross-view information-aggregation step across a directed network. By introducing signal-type weights and constructing an augmented interaction matrix , the authors prove almost-sure convergence to the true state under standard assumptions, and derive a mislearning-robustness condition that accommodates misleading signals. Theoretical results are complemented by numerical experiments in distributed localization tasks, demonstrating that integrating multiple viewpoints resolves observational ambiguities and enhances fault tolerance. The framework broadens the applicability of distributed inference to multi-feature environments and motivates future work on applying multiview social learning to high-dimensional, real-world sensor networks and multi-agent systems.

Abstract

Non-Bayesian social learning enables multiple agents to conduct networked signal and information processing through observing environmental signals and information aggregating. Traditional non-Bayesian social learning models only consider single signals, limiting their applications in scenarios where multiple viewpoints of information are available. In this work, we exploit, in the information aggregation step, the independently learned results from observations taken from multiple viewpoints and propose a novel non-Bayesian social learning model for scenarios with multiview observations. We prove the convergence of the model under traditional assumptions and provide convergence conditions for the algorithm in the presence of misleading signals. Through theoretical analyses and numerical experiments, we validate the strong reliability and robustness of the proposed algorithm, showcasing its potential for real-world applications.
Paper Structure (9 sections, 4 theorems, 22 equations, 6 figures)

This paper contains 9 sections, 4 theorems, 22 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Preliminaries and the model
  3. Problem formulation
  4. Social Learning Strategies with Multiple Signals
  5. Assumptions and results
  6. Numerical examples
  7. Learning with multiview observations
  8. Learning with misleading signal
  9. Conclusion and future work

Key Result

Lemma 1

If a Markov chain with finite states is irreducible, then it has a unique stationary distribution $\pi$. Let $A$ be the transition matrix of the Markov chain and further suppose it is aperiodic, then we have $\lim\limits_{k\rightarrow\infty}[A^k]_{ij}=\pi_j$, for $1\le i,j\le n$.

Figures (6)

  • Figure 1: An intuitive illustration for an understanding of the proposed algorithm.
  • Figure 2: The evolution of beliefs of Agent 1 on different states. (a) The two agents are unable to identify the underlying true state with a single type of signal. (b) The two agents achieve correct learning by combining the information from two types of signals.
  • Figure 3: Illustration of the scenario in Example 1. In this example, the two agents, due to the observational equivalence problem, cannot achieve correct learning relying solely on a single type of signal.
  • Figure 4: The evolution of beliefs of Agent 1 on all possible states in the first scenario of distributed cooperative localization task. (a) The agent can identify the optimal state solely based on azimuth information, but using only distance information results in erroneous learning. (b) By employing our algorithm to integrate the information from both types of signals, the beliefs of the agent converge to the true state.
  • Figure 5: The evolution of beliefs of Agent 1 on all possible states in the second scenario of distributed cooperative localization task. (a) The agents cannot achieve correct learning solely relying on distance or azimuth information. (b) By employing our algorithm to integrate the information from both types of signals, the agents can learn the underlying true state asymptotically.
  • ...and 1 more figures

Theorems & Definitions (9)

  • Lemma 1
  • Theorem 1
  • proof
  • Lemma 2
  • proof
  • Theorem 2
  • proof
  • Example 1
  • Example 2