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

Alexander V. Gasnikov, Ekaterina A. Krymova, Anastasia A. Lagunovskaya, Ilnura N. Usmanova, Fedor A. Fedorenko

Abstract: 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.