AsySPA: An Exact Asynchronous Algorithm for Convex Optimization Over Digraphs
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This paper proposes a novel exact asynchronous subgradient-push algorithm (AsySPA) to solve an additive cost optimization problem over digraphs where each node only has access to a local convex function and updates asynchronously with an arbitrary rate. Specifically, each node of a strongly connected digraph does not wait for updates from other nodes but simply starts a new update within any bounded time interval by using local information available from its in-neighbors. "Exact" means that every node of the AsySPA can asymptotically converge to the same optimal solution, even under different update rates among nodes and bounded communication delays. To compensate uneven update rates, we design a simple mechanism to adaptively adjust stepsizes per update in each node, which is substantially different from the existing works. Then, we construct a delay-free augmented system to address asynchrony and delays, and perform the convergence analysis by proposing a generalized subgradient algorithm, which clearly has its own significance and helps us to explicitly evaluate the convergence speed of the AsySPA. Finally, we demonstrate advantages of the AsySPA over the celebrated synchronous SPA in both theory and simulation.
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