Learning over Multitask Graphs -- Part II: Performance Analysis

TL;DR

This paper analyzes the steady-state performance of a multitask learning algorithm over networks, highlighting how network topology and regularization influence overall performance and stability conditions.

Contribution

It provides a detailed performance analysis of a diffusion-based multitask learning strategy, emphasizing the effects of network structure and regularization.

Findings

Network topology significantly affects steady-state performance.

Regularization strength impacts convergence and stability.

Explicit conditions for step-size and regularization ensure stability.

Abstract

Part I of this paper formulated a multitask optimization problem where agents in the network have individual objectives to meet, or individual parameter vectors to estimate, subject to a smoothness condition over the graph. A diffusion strategy was devised that responds to streaming data and employs stochastic approximations in place of actual gradient vectors, which are generally unavailable. The approach relied on minimizing a global cost consisting of the aggregate sum of individual costs regularized by a term that promotes smoothness. We examined the first-order, the second-order, and the fourth-order stability of the multitask learning algorithm. The results identified conditions on the step-size parameter, regularization strength, and data characteristics in order to ensure stability. This Part II examines steady-state performance of the strategy. The results reveal explicitly the influence of the network topology and the regularization strength on the network performance and provide insights into the design of effective multitask strategies for distributed inference over networks.