Systematic Analysis of Distributed Optimization Algorithms over Jointly-Connected Networks

We consider the distributed optimization problem, where a group of agents work together to optimize a common objective by communicating with neighboring agents and performing local computations. For a given algorithm, we use tools from robust control to systematically analyze the performance in the case where the communication network is time-varying. In particular, we assume only that the network is jointly connected over a finite time horizon (commonly referred to as B-connectivity), which does not require connectivity at each time instant. When applied to the distributed algorithm DIGing, our bounds are orders of magnitude tighter than those available in the literature.