Decentralized stochastic optimization algorithms using uncoordinated step-sizes over unbalanced directed networks

Abstract

Decentralized stochastic gradient methods play significant roles in large-scale optimization that finds many practical applications in signal processing, machine learning, and coordinated control. In this short communication, we focus on studying large-scale convex optimization problems over multi-agent systems, where the mutual goal of agents in the network is to optimize a global objective function expressed as a sum of local objective functions. Each agent in the system uses only local computation and communication in the overall process without leaking their private information. We first introduce both the local stochastic averaging gradient method and the local stochastic variance-reduced gradient method into decentralized convex optimization (DCO) over unbalanced directed networks. Then, in order to increase the autonomy and flexibility of the agents, uncoordinated step-sizes are considered. Based on the well-known variance-reduced stochastic gradient methods and uncoordinated step-sizes, we propose two fully decentralized algorithms named SAGA-UDN and SVRG-UDN for DCO over unbalanced directed networks, respectively. Finally, both SAGA-UDN and SVRG-UDN are numerically studied under various network parameters and objective functions. Some real-world data sets are used in simulations to demonstrate the improved performance of SAGA-UDN and SVRG-UDN.