Socially Inspired Adaptive Framework for Distributed Online Inference

Collective decision-making in networked systems is often shaped not only by peer interactions but also by persistent external influences. This paper introduces an intervened non-Bayesian social learning model that explicitly incorporates external information sources—whose beliefs remain fixed and potentially biased—into the belief-update process of a distributed multi-agent network. Analytical characterization of the proposed model reveals that such interventions disrupt strong consensus on the underlying true state, resulting in steady-state belief distributions that exhibit persistent oscillation and even polarization, consistent with empirical social observations. Building upon these insights, we propose a socially inspired adaptive algorithm for distributed online inference, which mitigates the rigidity of traditional non-Bayesian social learning updates and enables agents to remain responsive to environmental changes. Theoretical analysis and numerical experiments demonstrate that the proposed framework achieves enhanced adaptability and accurate online inference while preserving the decentralized cooperation mechanism of non-Bayesian social learning.