Push-LSVRG-UP: Distributed Stochastic Optimization Over Unbalanced Directed Networks With Uncoordinated Triggered Probabilities

Distributed stochastic optimization, arising in the crossing and integration of traditional distributed computing storage, network science, has advantages high efficiency a low per-iteration computational complexity resolving large-scale optimization problems. This paper concentrates on convex finite-sum problem multi-agent system over unbalanced directed networks. To tackle this an efficient way, consensus algorithm, adopting push-sum technique loopless variance-reduced gradient (LSVRG) method with uncoordinated triggered probabilities, is developed named Push-LSVRG-UP. Each agent under algorithmic framework performs only local computation communicates its neighbors without leaking their private information. The convergence analysis Push-LSVRG-UP relied analyzing contraction relationships between four error terms associated system. Theoretical results provide explicit feasible range constant step-size, linear rate, iteration when achieving globally optimal solution. It shown that achieves superior characteristics accelerated convergence, fewer storage costs, lower than most existing works. Meanwhile, introduction probabilistic mechanism allows to facilitate independence flexibility agents batch gradients. In simulations, practicability improved performance are manifested via two learning problems based real-world datasets.