A Distributed Optimization Algorithm over Time-Varying Graphs with Efficient Gradient Evaluations

Abstract: We propose an algorithm for distributed optimization over time-varying communication networks. Our algorithm uses an optimized ratio between the number of rounds of communication and gradient evaluations to achieve fast convergence. The iterates converge to the global optimizer at the same rate as centralized gradient descent when measured in terms of the number of gradient evaluations while using the minimum number of communications to do so. Furthermore, the iterates converge at a near-optimal rate when measured in terms of the number of communication rounds. We compare our algorithm with several other known algorithms on a distributed target localization problem.