Stochastic online optimization. Single-point and multi-point non-linear multi-armed bandits. Convex and strongly-convex case


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In this paper the gradient-free modification of the mirror descent method for convex stochastic online optimization problems is proposed. The crucial assumption in the problem setting is that function realizations are observed with minor noises. The aim of this paper is to derive the convergence rate of the proposed methods and to determine a noise level which does not significantly affect the convergence rate.

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A. Gasnikov

Moscow Institute of Physics and Technology (State University); Institute for Information Transmission Problems (Kharkevich Institute)

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Email: gasnikov@yandex.ru
俄罗斯联邦, Moscow; Moscow

E. Krymova

Institute for Information Transmission Problems (Kharkevich Institute)

Email: gasnikov@yandex.ru
俄罗斯联邦, Moscow

A. Lagunovskaya

Keldysh Institute of Applied Mathematics; Moscow Institute of Physics and Technology (State University)

Email: gasnikov@yandex.ru
俄罗斯联邦, Moscow; Moscow

I. Usmanova

Moscow Institute of Physics and Technology (State University); Institute for Information Transmission Problems (Kharkevich Institute)

Email: gasnikov@yandex.ru
俄罗斯联邦, Moscow; Moscow

F. Fedorenko

Moscow Institute of Physics and Technology (State University)

Email: gasnikov@yandex.ru
俄罗斯联邦, Moscow

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