Information-theoretic lower bounds on the oracle complexity of stochastic convex optimization

TL;DR

This paper investigates the fundamental limits of stochastic convex optimization complexity using an oracle model, providing tight minimax bounds that enhance understanding of the problem's inherent difficulty.

Contribution

It offers the first tight minimax complexity estimates for stochastic convex optimization across various function classes, advancing theoretical understanding.

Findings

Established tight minimax complexity bounds for stochastic convex optimization.

Improved upon previous results in the oracle complexity of convex problems.

Highlights the fundamental hardness of stochastic convex optimization in an oracle model.

Abstract

Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardness of these problems. Given the extensive use of convex optimization in machine learning and statistics, gaining an understanding of these complexity-theoretic issues is important. In this paper, we study the complexity of stochastic convex optimization in an oracle model of computation. We improve upon known results and obtain tight minimax complexity estimates for various function classes.