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Gradient-Free Two-Point Methods for Solving Stochastic Nonsmooth Convex Optimization Problems with Small Non-Random Noises

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Abstract

We study nonsmooth convex stochastic optimization problems with a two-point zero-order oracle, i.e., at each iteration one can observe the values of the function’s realization at two selected points. These problems are first smoothed out with the well-known technique of double smoothing (B.T. Polyak) and then solved with the stochastic mirror descent method. We obtain conditions for the permissible noise level of a nonrandom nature exhibited in the computation of the function’s realization for which the estimate on the method’s rate of convergence is preserved.

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Correspondence to A. S. Bayandina.

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Original Russian Text © A.S. Bayandina, A.V. Gasnikov, A.A. Lagunovskaya, 2018, published in Avtomatika i Telemekhanika, 2018, No. 8, pp. 38–49.

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Bayandina, A.S., Gasnikov, A.V. & Lagunovskaya, A.A. Gradient-Free Two-Point Methods for Solving Stochastic Nonsmooth Convex Optimization Problems with Small Non-Random Noises. Autom Remote Control 79, 1399–1408 (2018). https://doi.org/10.1134/S0005117918080039

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