2024/06/14 by Ellie Pond, April Sebok, Pond, Ellie +5
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2406.10124
openalex publication_date 2024/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a totally asynchronous algorithm for convex optimization that is based on a novel generalization of Nesterov's accelerated gradient method. This algorithm is developed for fast convergence under "total asynchrony," i.e., allowing arbitrarily long delays between agents' computations and communications without assuming any form of delay bound. These conditions may arise, for example, due to jamming by adversaries. Our framework is block-based, in the sense that each agent is only responsible for computing updates to (and communicating the values of) a small subset of the network-level decision variables. In our main result, we present bounds on the algorithm's parameters that guarantee linear convergence to an optimizer. Then, we quantify the relationship between (i) the total number of computations and communications executed by the agents and (ii) the agents' collective distance to an optimum. Numerical simulations show that this algorithm requires 28% fewer iterations than the heavy ball algorithm and 61% fewer iterations than gradient descent under total asynchrony.