Learning halfspaces with the zero-one loss: Time-accuracy tradeoffs

Aharon Birnbaum, Shai Shalev-Shwartz

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

11 Scopus citations

Abstract

Given α, ε, we study the time complexity required to improperly learn a halfs-pace with misclassification error rate of at most (1 + α)L*gamma + ε, where L *gamma is the optimal γ-margin error rate. For α = 1/γ, polynomial time and sample complexity is achievable using the hinge-loss. For α = 0, Shalev-Shwartz et al. [2011] showed that poly(1/γ) time is impossible, while learning is possible in time exp(Õ (1/γ)). An immediate question, which this paper tackles, is what is achievable if α ε (0, 1/γ). We derive positive results interpolating between the polynomial time for α = 1/γ and the exponential time for α = 0. In particular, we show that there are cases in which α = o(1/γ) but the problem is still solvable in polynomial time. Our results naturally extend to the adversarial online learning model and to the PAC learning with malicious noise model.

Original languageAmerican English
Title of host publicationAdvances in Neural Information Processing Systems 25
Subtitle of host publication26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012
Pages926-935
Number of pages10
StatePublished - 2012
Event26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012 - Lake Tahoe, NV, United States
Duration: 3 Dec 20126 Dec 2012

Publication series

NameAdvances in Neural Information Processing Systems
Volume2
ISSN (Print)1049-5258

Conference

Conference26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012
Country/TerritoryUnited States
CityLake Tahoe, NV
Period3/12/126/12/12

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