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Distributed Strongly Convex Optimization

A lot of effort has been invested into characterizing the convergence rates of gradient based algorithms for non-linear convex optimization. Recently, motivated by large datasets and problems in machine learning, the interest has shifted towards distributed optimization. In this work we present a distributed algorithm for strongly convex constrained optimization. Each node in a network of n computers converges to the optimum of a strongly convex, L-Lipchitz continuous, separable objective at a rate O(log (sqrt(n) T) / T) where T is the number of iterations. This rate is achieved in the online setting where the data is revealed one at a time to the nodes, and in the batch setting where each node has access to its full local dataset from the start. The same convergence rate is achieved in expectation when the subgradients used at each node are corrupted with additive zero-mean noise.