Learning kernel-based halfspaces with the zero-one loss

Shai Shalev-Shwartz, Ohad Shamir, Karthik Sridharan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

11 Scopus citations

Abstract

We describe and analyze a new algorithm for agnostically learning kernel-based halfspaces with respect to the zero-one loss function. Unlike most previous formulations which rely on surrogate convex loss functions (e.g. hinge-loss in SVM and log-loss in logistic regression), we provide finite time/sample guarantees with respect to the more natural zero-one loss function. The proposed algorithm can learn kernel-based halfspaces in worst-case time poly (exp (L log(L/ε))), for any distribution, where L is a Lipschitz constant (which can be thought of as the reciprocal of the margin), and the learned classifier is worse than the optimal halfspace by at most ε. We also prove a hardness result, showing that under a certain cryptographic assumption, no algorithm can learn kernel-based halfspaces in time polynomial in L.

Original languageAmerican English
Title of host publicationCOLT 2010 - The 23rd Conference on Learning Theory
Pages441-450
Number of pages10
StatePublished - 2010
Event23rd Conference on Learning Theory, COLT 2010 - Haifa, Israel
Duration: 27 Jun 201029 Jun 2010

Publication series

NameCOLT 2010 - The 23rd Conference on Learning Theory

Conference

Conference23rd Conference on Learning Theory, COLT 2010
Country/TerritoryIsrael
CityHaifa
Period27/06/1029/06/10

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