Accelerated gradient sliding and variance reduction

Abstract: We consider sum-type strongly convex optimization problem (first term) with smooth convex not proximal friendly composite (second term). We show that the complexity of this problem can be split into optimal number of incremental oracle calls for the first (sum-type) term and optimal number of oracle calls for the second (composite) term. Here under `optimal number' we mean estimate that corresponds to the well known lower bound in the absence of another term.