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

Alekh Agarwal(alekh***at***cs.berkeley.edu)
Peter L Bartlett(peter***at***berkeley.edu)
Pradeep Ravikumar(pradeepr***at***cs.utexas.edu)
Martin J Wainwright(wainwrig***at***stat.berkeley.edu)

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.

Keywords: Convex optimization, oracle complexity

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Stochastic Programming

Citation: ArXiv tech report, arXiv:1009.0571v1 http://arxiv.org/abs/1009.0571

Download: [PDF]

Entry Submitted: 09/06/2010
Entry Accepted: 09/06/2010
Entry Last Modified: 09/06/2010

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