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Accelerated First-Order Optimization Algorithms for Machine Learning

Numerical optimization serves as one of the pillars of machine learning. To meet the demands of big data applications, lots of efforts have been put on designing theoretically and practically fast algorithms. This article provides a comprehensive survey on accelerated first-order algorithms with a focus on stochastic algorithms. Specifically, this article starts with reviewing the basic accelerated algorithms on deterministic convex optimization, then concentrates on their extensions to stochastic convex optimization, and at last introduces some recent developments on acceleration for nonconvex optimization.