Gossip Dual Averaging for Decentralized Optimization of Pairwise Functions

TL;DR

This paper introduces gossip dual averaging algorithms for decentralized optimization of pairwise functions, applicable to various tasks like ranking and metric learning, with theoretical convergence guarantees and practical effectiveness demonstrated through simulations.

Contribution

It proposes a flexible gossip dual averaging framework for decentralized pairwise function optimization, handling both synchronous and asynchronous settings with convergence analysis.

Findings

Algorithms preserve centralized convergence rates with an additive bias.

Numerical simulations show effectiveness in AUC maximization and metric learning.

Framework accommodates constrained and regularized optimization variants.

Abstract

In decentralized networks (of sensors, connected objects, etc.), there is an important need for efficient algorithms to optimize a global cost function, for instance to learn a global model from the local data collected by each computing unit. In this paper, we address the problem of decentralized minimization of pairwise functions of the data points, where these points are distributed over the nodes of a graph defining the communication topology of the network. This general problem finds applications in ranking, distance metric learning and graph inference, among others. We propose new gossip algorithms based on dual averaging which aims at solving such problems both in synchronous and asynchronous settings. The proposed framework is flexible enough to deal with constrained and regularized variants of the optimization problem. Our theoretical analysis reveals that the proposed algorithms preserve the convergence rate of centralized dual averaging up to an additive bias term. We present numerical simulations on Area Under the ROC Curve (AUC) maximization and metric learning problems which illustrate the practical interest of our approach.