Affine-invariant online optimization and the low-rank experts problem

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We present a new affine-invariant optimization algorithm called Online Lazy Newton. The regret of Online Lazy Newton is independent of conditioning: the algorithm's performance depends on the best possible preconditioning of the problem in retrospect and on its intrinsic dimensionality. As an application, we show how Online Lazy Newton can be used to achieve an optimal regret of order √rT for the low-rank experts problem, improving by a √r factor over the previously best known bound and resolving an open problem posed by Hazan et al. [15].

Original languageEnglish
Pages (from-to)4748-4756
Number of pages9
JournalAdvances in Neural Information Processing Systems
StatePublished - 2017
Externally publishedYes
Event31st Annual Conference on Neural Information Processing Systems, NIPS 2017 - Long Beach, United States
Duration: 4 Dec 20179 Dec 2017

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