Resilient Distributed Min-Max Optimization under Byzantine Network Attacks

This paper studies a resilient algorithmic framework for solving the distributed min-max optimization problem against network communication attacks. Our algorithm builds on two key ingredients: i) a resilient convex combination scheme which helps eliminate the malicious information injected by the unidentifiable network attacks; and ii) a consensus-based distributed algorithm which solves min-max optimization over time-varying unbalanced directed graphs. We show that, under reasonable assumptions, e.g., attacked communication channels can be recovered within a certain time-window, the proposed algorithm converges to the exact global optimal solution which involves every attacked/non-attacked agent within the network. This result is primarily different from the existing relevant works whose the objective only includes local cost functions at the non-attacked agents.