Information-theoretic lower bounds on the oracle complexity of stochastic convex optimization
Machine Learning
2011-11-22 v3 Systems and Control
Optimization and Control
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.
Cite
@article{arxiv.1009.0571,
title = {Information-theoretic lower bounds on the oracle complexity of stochastic convex optimization},
author = {Alekh Agarwal and Peter L. Bartlett and Pradeep Ravikumar and Martin J. Wainwright},
journal= {arXiv preprint arXiv:1009.0571},
year = {2011}
}