2023/05/01 by Duong Thuy Anh Nguyen, Duong Tung Nguyen, Nguyen, Duong Thuy Anh +3 · 2 citations
Computer Science · Engineering · Mathematics · #Distributed Control Multi-Agent Systems #FOS: Mathematics #Mathematical Biology Tumor Growth #Molecular Communication and Nanonetworks #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2305.00629
openalex publication_date 2023/05/01 · openalex created_date 2023/05/03 · openalex updated_date 2026/07/28
We study a distributed method called SAB-TV, which employs gradient tracking to collaboratively minimize the sum of smooth and strongly-convex local cost functions for networked agents communicating over a time-varying directed graph. Each agent, assumed to have access to a stochastic first-order oracle for obtaining an unbiased estimate of the gradient of its local cost function, maintains an auxiliary variable to asymptotically track the stochastic gradient of the global cost. The optimal decision and gradient tracking are updated over time through limited information exchange with local neighbors using row- and column-stochastic weights, guaranteeing both consensus and optimality. With a sufficiently small constant step-size, we demonstrate that, in expectation, SAB-TV converges linearly to a neighborhood of the optimal solution. Numerical simulations illustrate the effectiveness of the proposed algorithm.