Robust Online Learning over Networks

TL;DR

This paper introduces DOT-ADMM, a robust distributed online learning algorithm for multi-agent networks that handles data variability, asynchronous updates, communication issues, and inexact computations, with proven linear convergence under certain conditions.

Contribution

It develops and analyzes DOT-ADMM, a novel operator-theoretic approach for robust, convergent online distributed learning in challenging network environments.

Findings

DOT-ADMM converges linearly under metric subregularity.

The algorithm is robust to data changes, asynchrony, communication unreliability, and inexact computations.

Numerical results show superior performance compared to existing methods.

Abstract

The recent deployment of multi-agent networks has enabled the distributed solution of learning problems, where agents cooperate to train a global model without sharing their local, private data. This work specifically targets some prevalent challenges inherent to distributed learning: (i) online training, i.e., the local data change over time; (ii) asynchronous agent computations; (iii) unreliable and limited communications; and (iv) inexact local computations. To tackle these challenges, we apply the Distributed Operator Theoretical (DOT) version of the Alternating Direction Method of Multipliers (ADMM), which we call "DOT-ADMM". We prove that if the DOT-ADMM operator is metric subregular, then it converges with a linear rate for a large class of (not necessarily strongly) convex learning problems toward a bounded neighborhood of the optimal time-varying solution, and characterize how such neighborhood depends on (i)-(iv). We first derive an easy-to-verify condition for ensuring the metric subregularity of an operator, followed by tutorial examples on linear and logistic regression problems. We corroborate the theoretical analysis with numerical simulations comparing DOT-ADMM with other state-of-the-art algorithms, showing that only the proposed algorithm exhibits robustness to (i)-(iv).