2024/08/05 by Doostmohammadian, Mohammadreza, Gabidullina, Zulfiya R., Rabiee, Hamid R. · 1 citation
#Distributed #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Parallel #Signal Processing (eess.SP) #Systems and Control (eess.SY) #and Cluster Computing (cs.DC) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2408.02269
Decentralized optimization strategies are helpful for various applications, from networked estimation to distributed machine learning. This paper studies finite-sum minimization problems described over a network of nodes and proposes a computationally efficient algorithm that solves distributed convex problems and optimally finds the solution to locally non-convex objective functions. In contrast to batch gradient optimization in some literature, our algorithm is on a single-time scale with no extra inner consensus loop. It evaluates one gradient entry per node per time. Further, the algorithm addresses link-level nonlinearity representing, for example, logarithmic quantization of the exchanged data or clipping of the exchanged data bits. Leveraging perturbation-based theory and algebraic Laplacian network analysis proves optimal convergence and dynamics stability over time-varying and switching networks. The time-varying network setup might be due to packet drops or link failures. Despite the nonlinear nature of the dynamics, we prove exact convergence in the face of odd sign-preserving sector-bound nonlinear data transmission over the links. Illustrative numerical simulations further highlight our contributions.