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

## TL;DR

This paper analyzes how agents in a network can reliably learn a parameter over time despite changing connections and decaying influence, by establishing conditions for convergence.

## Contribution

It introduces a necessary and sufficient condition for the decay rate of influence weights that guarantees successful social learning in dynamic, directed networks.

## Key findings

- Convergence is achievable under specific decay rate conditions.
- Decaying influence weights do not prevent social learning if conditions are met.
- The network's connectivity over finite intervals is sufficient for learning.

## Abstract

We study the convergence of the log-linear non-Bayesian social learning update rule, for a group of agents that collectively seek to identify a parameter that best describes a joint sequence of observations. Contrary to recent literature, we focus on the case where agents assign decaying weights to its neighbors, and the network is not connected at every time instant but over some finite time intervals. We provide a necessary and sufficient condition for the rate at which agents decrease the weights and still guarantees social learning.