Distributed Personalized Gradient Tracking with Convex Parametric Models

TL;DR

This paper introduces a distributed optimization algorithm that combines gradient tracking and recursive parameter estimation to solve personalized online problems over networks, with proven bounded regret.

Contribution

It proposes a novel distributed algorithm integrating gradient tracking and recursive least squares for personalized optimization with theoretical guarantees.

Findings

Algorithm achieves bounded regret under certain conditions.

Numerical example confirms theoretical results.

Effectively learns user-specific parameters online.

Abstract

We present a distributed optimization algorithm for solving online personalized optimization problems over a network of computing and communicating nodes, each of which linked to a specific user. The local objective functions are assumed to have a composite structure and to consist of a known time-varying (engineering) part and an unknown (user-specific) part. Regarding the unknown part, it is assumed to have a known parametric (e.g., quadratic) structure a priori, whose parameters are to be learned along with the evolution of the algorithm. The algorithm is composed of two intertwined components: (i) a dynamic gradient tracking scheme for finding local solution estimates and (ii) a recursive least squares scheme for estimating the unknown parameters via user's noisy feedback on the local solution estimates. The algorithm is shown to exhibit a bounded regret under suitable assumptions. Finally, a numerical example corroborates the theoretical analysis.