Decentralized Adversarial Training over Graphs

The vulnerability of machine learning models to adversarial attacks has been attracting considerable attention in recent years. Most existing studies focus on the behavior of stand-alone single-agent learners. In comparison, this work studies adversarial training over graphs, where individual agents are subjected to perturbations of varied strength levels across space. It is expected that interactions by linked agents, and the heterogeneity of the attack models that are possible over the graph, can help enhance robustness in view of the coordination power of the group. Using a min-max formulation of distributed learning, we develop a decentralized adversarial training framework for multi-agent systems. Specifically, we devise two decentralized adversarial training algorithms by relying on two popular decentralized learning strategies--diffusion and consensus. We analyze the convergence properties of the proposed framework for strongly-convex, convex, and non-convex environments, and illustrate the enhanced robustness to adversarial attacks.