Accelerated Row-stochastic Optimization over Directed Graphs with Uncoordinated Step Sizes

摘要

This paper investigates a distributed optimization problem over a multiagent network, in which the target of agents is to collaboratively optimize the sum of all local objective functions. The case discusses that the network topology among agents is described by a strongly connected directed graph. The proposed algorithm utilizes row-stochastic weight matrices and uncoordinated step sizes. Under conditions that the objective functions are strong convex, and have Lipschitz continuous gradients, we manifest that proposed algorithm faster linearly converges to the global optimization solution than other algorithms as long as the chosen step sizes do not exceed an exact characterized upper bound. Numerical experiments are also provided to testify the theoretical analysis.