Distributed Statistical Min-Max Learning in the Presence of Byzantine Agents

TL;DR

This paper introduces a robust distributed algorithm for min-max learning that effectively handles Byzantine adversarial agents, providing near-optimal convergence guarantees in a multi-agent setting.

Contribution

It proposes the first formal theoretical framework for large-scale distributed min-max learning with Byzantine adversaries, using a robust variant of the extra-gradient algorithm.

Findings

Achieves near-optimal convergence rates for smooth convex-concave functions.

Demonstrates the impact of adversarial corruption on convergence.

Shows the benefits of collaboration among non-faulty agents.

Abstract

Recent years have witnessed a growing interest in the topic of min-max optimization, owing to its relevance in the context of generative adversarial networks (GANs), robust control and optimization, and reinforcement learning. Motivated by this line of work, we consider a multi-agent min-max learning problem, and focus on the emerging challenge of contending with worst-case Byzantine adversarial agents in such a setup. By drawing on recent results from robust statistics, we design a robust distributed variant of the extra-gradient algorithm - a popular algorithmic approach for min-max optimization. Our main contribution is to provide a crisp analysis of the proposed robust extra-gradient algorithm for smooth convex-concave and smooth strongly convex-strongly concave functions. Specifically, we establish statistical rates of convergence to approximate saddle points. Our rates are near-optimal, and reveal both the effect of adversarial corruption and the benefit of collaboration among the non-faulty agents. Notably, this is the first paper to provide formal theoretical guarantees for large-scale distributed min-max learning in the presence of adversarial agents.