Optimal Aggregation Strategies for Social Learning over Graphs

TL;DR

This paper analyzes how combination policies affect the performance of adaptive social learning over graphs, deriving bounds on error probabilities and highlighting the importance of steady-state optimization.

Contribution

It introduces a large-deviation analysis framework to optimize combination policies for improved steady-state performance in social learning.

Findings

Optimal Perron eigenvector selection improves steady-state error bounds

Combination policies have minimal impact on transient adaptation time

Steady-state performance is more influenced by policy choice than transient behavior

Abstract

Adaptive social learning is a useful tool for studying distributed decision-making problems over graphs. This paper investigates the effect of combination policies on the performance of adaptive social learning strategies. Using large-deviation analysis, it first derives a bound on the steady-state error probability and characterizes the optimal selection for the Perron eigenvectors of the combination policies. It subsequently studies the effect of the combination policy on the transient behavior of the learning strategy by estimating the adaptation time in the low signal-to-noise ratio regime. In the process, it is discovered that, interestingly, the influence of the combination policy on the transient behavior is insignificant, and thus it is more critical to employ policies that enhance the steady-state performance. The theoretical conclusions are illustrated by means of computer simulations.