Polynomial convergence of iterations of certain random operators in Hilbert space
Copyright policy )Polynomial convergence of iterations of certain random operators in Hilbert space
Abstract We study the convergence of a random iterative sequence of a family of operators on infinite-dimensional Hilbert spaces, inspired by the stochastic gradient descent (SGD) algorithm in the case of the noiseless regression. We identify conditions that are strictly broader than previously known for polynomial convergence rate in various norms, and characterize the roles the randomness plays in determining the best multiplicative constants. Additionally, we prove almost sure convergence of the sequence.
FOS: Computer and information sciences, Computer Science - Machine Learning, random operators, polynomial convergence, Functional Analysis (math.FA), Machine Learning (cs.LG), Mathematics - Functional Analysis, 46N10, 47B80, 60B10, FOS: Mathematics, Applications of operator theory in optimization, convex analysis, mathematical programming, economics, Convergence of probability measures, Random linear operators, stochastic gradient descent algorithm
FOS: Computer and information sciences, Computer Science - Machine Learning, random operators, polynomial convergence, Functional Analysis (math.FA), Machine Learning (cs.LG), Mathematics - Functional Analysis, 46N10, 47B80, 60B10, FOS: Mathematics, Applications of operator theory in optimization, convex analysis, mathematical programming, economics, Convergence of probability measures, Random linear operators, stochastic gradient descent algorithm
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