Robust Online Learning over Networks
Nicola Bastianello, Diego Deplano, Mauro Franceschelli, Karl H. Johansson
TL;DR
The work tackles distributed online learning over networks with asynchronous updates, unreliable communications, and inexact local computations by introducing DOT-ADMM, a relaxed ADMM variant. It proves linear convergence in mean to a neighborhood of the time-varying optimum under metric subregularity of the DOT-ADMM operator, and provides an easily verifiable condition (Proposition ULaffMS) to certify this property for common losses. The methodology is demonstrated on linear, robust linear, and logistic regression, with numerical experiments showing robust performance under packet losses, quantization, and data shifts, outperforming gradient-tracking and DGD baselines. The results extend convergence guarantees beyond strongly convex settings, offering practical relevance for privacy-preserving, networked learning in dynamic environments.
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).