Anastasia Lagunovskaya

Gradient-free proximal methods with inexact oracle for convex stochastic nonsmooth optimization problems on the simplex

In this paper we propose a modification of the mirror descent method for non-smooth stochastic convex optimization problems on the unit simplex. The optimization problems considered differ from the classical ones by availability of function values realizations. Our purpose is to derive the convergence rate of the method proposed and to determine the level of noise that does not significantly affect the convergence rate.

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

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.

Gradient-Free Two-Point Methods for Solving Stochastic Nonsmooth Convex Optimization Problems with Small Non-Random Noises

We study nonsmooth convex stochastic optimization problems with a two-point zero-order oracle, i.e., at each iteration one can observe the values of the function’s realization at two selected points. These problems are first smoothed out with the well-known technique of double smoothing (B.T. Polyak) and then solved with the stochastic mirror descent method. We obtain conditions for the permissible noise level of a nonrandom nature exhibited in the computation of the function’s realization for which the estimate on the method’s rate of convergence is preserved.