Oracle Complexity of Second-Order Methods for Finite-Sum Problems.

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Abstract

Finite-sum optimization problems are ubiquitous in machine learning, and are commonly solved using first-order methods which rely on gradient computations. Recently, there has been growing interest in second-order methods, which rely on both gradients and Hessians. In principle, second-order methods can require much fewer iterations than first-order methods, and hold the promise for more efficient algorithms. Although computing and manipulating Hessians is prohibitive for high-dimensional problems in general, the Hessians of individual functions in finite-sum problems can often be efficiently computed, e.g. because they possess a low-rank structure. Can second-order information indeed be used to solve such problems more efficiently? In this paper, we provide evidence that the answer – perhaps surprisingly – is negative, at least in terms of worst-case guarantees. However, we also discuss what additional assumptions and algorithmic approaches might potentially circumvent this negative result.
Original languageEnglish
Title of host publicationICML 2017
Pages205-213
Number of pages9
StatePublished - 2017
Event34th International Conference on Machine Learning, ICML 2017 - Sydney, Australia
Duration: 6 Aug 201711 Aug 2017

Publication series

NameProceedings of Machine Learning Research
PublisherPMLR
Volume70

Conference

Conference34th International Conference on Machine Learning, ICML 2017
Country/TerritoryAustralia
CitySydney
Period6/08/1711/08/17

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