Asynchronous Gossip Algorithm for Stochastic Optimization with Approximate Projections: Constant Stepsize Analysis

This paper considers the problem of minimizing the sum of convex functions over a network when each component function is known (with stochastic errors) to a specific network agent. We need to note that the objective function is strongly convex in this paper. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact projections. Hence, We propose an asynchronous gossip-based algorithm with approximate projections. We investigate the convergence properties of the algorithm for a constant stepsize, where each agent chooses its own stepsize independently of the other agents. We establish some error bounds on the expected distance from the optimal point and the expected function value. We also provide the detailed proofs in this paper.

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