In the paper we generalize universal gradient method (Yu. Nesterov) to strongly convex case and to Intermediate gradient method (Devolder-Glineur-Nesterov). We also consider possible generalizations to stochastic and online context. We show how these results can be generalized to gradient-free method and method of random direction search. But the main ingridient of this paper is assumption about the oracle. We considered the oracle to be inexact.
@article{arxiv.1502.06259,
title = {Gradient and gradient-free methods for stochastic convex optimization with inexact oracle},
author = {Alexander Gasnikov and Pavel Dvurechensky and Dmitry Kamzolov},
journal= {arXiv preprint arXiv:1502.06259},
year = {2016}
}