  In this paper, we consider smooth convex optimization problems with simple
constraints and inexactness in the oracle information such as value, partial or
directional derivatives of the objective function. We introduce a unifying
framework, which allows to construct different types of accelerated randomized
methods for such problems and to prove convergence rate theorems for them. We
focus on accelerated random block-coordinate descent, accelerated random
directional search, accelerated random derivative-free method and, using our
framework, provide their versions for problems with inexact oracle information.
Our contribution also includes accelerated random block-coordinate descent with
inexact oracle and entropy proximal setup as well as derivative-free version of
this method. Moreover, we present an extension of our framework for strongly
convex optimization problems. We also discuss an extension for the case of
inexact model of the objective function.
