Accelerated gradient sliding and variance reduction

TL;DR

This paper introduces a method to efficiently solve sum-type strongly convex optimization problems by separately optimizing the number of oracle calls for each component, achieving optimal complexity bounds.

Contribution

It presents a novel approach that splits the complexity analysis for sum-type problems into separate optimal bounds for each term, improving efficiency in convex optimization.

Findings

Achieves optimal oracle call complexity for sum-type terms.

Provides a theoretical framework for splitting complexity in composite problems.

Matches known lower bounds in the absence of the other term.

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.