Resilient Distributed Optimization

Abstract

This paper considers a distributed optimization problem in the presence of Byzantine agents capable of introducing untrustworthy information into the communication network. A resilient distributed subgradient algorithm is proposed based on graph redundancy and objective redundancy. It is shown that the algorithm causes all non-Byzantine agents' states to asymptotically converge to the same optimal point under appropriate assumptions. A partial convergence rate result is also provided.

This version fixes the incorrect statements of Proposition 3 and Theorem 2 in the last version