Maximal Dissent: A State-Dependent Way to Agree in Distributed Convex Optimization

Consider a set of agents collaboratively solving a distributed convex optimization problem asynchronously under stringent communication constraints. When an agent becomes active, it is allowed to communicate with only one of its neighbors. In this article, we propose new state-dependent gossip algorithms where the agents with maximal dissent average their estimates. We prove the almost sure convergence of max-dissent subgradient methods using a unified framework applicable to other state-dependent distributed optimization algorithms. Furthermore, our proof technique bypasses the need to establish the information flow between any two agents within a time interval of uniform length by intelligently studying the convergence properties of the Lyapunov function used in our analysis.