Geodesic
A note on the convergence rate in regularized stochastic programming
Kybernetika, Tome 57 (2021) no. 1, pp. 38-45.

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We deal with a stochastic programming problem that can be inconsistent. To overcome the inconsistency we apply Tikhonov's regularization technique, and, using recent results on the convergence rate of empirical measures in Wasserstein metric, we treat the following two related problems: 1. A choice of regularization parameters that guarantees the convergence of the minimization procedure. 2. Estimation of the rate of convergence in probability. Considering both light and heavy tail distributions and Lipschitz objective functions (which can be unbounded), we obtain the power bounds for the convergence rate.
DOI : 10.14736/kyb-2021-1-0038
Classification : 90C15
Keywords: stochastic programming problem; Tikhonov's regularization; Lipschitz conditions; Kantorovich metric; convergence rate 
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Gordienko, Evgueni; Gryazin, Yury. A note on the convergence rate in regularized stochastic programming. Kybernetika, Tome 57 (2021) no. 1, pp. 38-45. doi : 10.14736/kyb-2021-1-0038. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2021-1-0038/

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