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

• URL: http://arxiv.org/abs/2204.03187v1
• Date: Thu, 7 Apr 2022 03:36:28 GMT
• Title: Distributed Statistical Min-Max Learning in the Presence of Byzantine Agents
• Authors: Arman Adibi, Aritra Mitra, George J. Pappas and Hamed Hassani
• Abstract summary: We consider a multi-agent min-max learning problem, and focus on the emerging challenge of contending with Byzantine adversarial agents. 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. Our rates are near-optimal, and reveal both the effect of adversarial corruption and the benefit of collaboration among the non-faulty agents.
• Score: 34.46660729815201
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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