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arXiv · 1412.3890

Gradient-free prox-methods with inexact oracle for stochastic convex optimization problems on a simplex

Alexander Gasnikov·Anastasia Lagunovskaya·Ilnura Usmanova·Fedor Fedorenko
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Abstract

In the paper we show that euclidian randomization in some situations (i.e. for gradient-free method on a simplex) can be as good as the randomization on the unit sphere in 1-norm. That is on the simplex example we show that for gradient-free methods the choise of the prox-structure and the choise of a way of randomization have to be connected to each other. We demonstrate how it can be done in an optimal way. It is important that we consider inexact oracle.

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Alexander Gasnikov, Anastasia Lagunovskaya, Ilnura Usmanova, Fedor Fedorenko. 2014-12-12. Gradient-free prox-methods with inexact oracle for stochastic convex optimization problems on a simplex. https://arxiv.org/abs/1412.3890

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