Learning rotations with little regret

We describe online algorithms for learning a rotation from pairs of unit vectors in R n . We show that the expected regret of our online algorithm compared to the best fixed rotation chosen offline over T iterations is n T . We also give a lower bound that proves that this expected regret bound is o...

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Bibliographic Details
Published inMachine learning Vol. 104; no. 1; pp. 129 - 148
Main Authors Hazan, Elad, Kale, Satyen, Warmuth, Manfred K.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.07.2016
Springer Nature B.V
Subjects
Algorithms
Artificial Intelligence
Computer Science
Constants
Control
Learning
Mathematical analysis
Mechatronics
Natural Language Processing (NLP)
Online
Optimization
Robotics
Simulation and Modeling
Texts
Vectors (mathematics)
Minimax
Regret bounds
Online learning
Rotations
Bregman projection
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Summary:We describe online algorithms for learning a rotation from pairs of unit vectors in R n . We show that the expected regret of our online algorithm compared to the best fixed rotation chosen offline over T iterations is n T . We also give a lower bound that proves that this expected regret bound is optimal within a constant factor. This resolves an open problem posed in COLT 2008. Our online algorithm for choosing a rotation matrix is essentially an incremental gradient descent algorithm over the set of all matrices, with specially tailored projections. We also show that any deterministic algorithm for learning rotations has Ω ( T ) regret in the worst case.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0885-6125
1573-0565
DOI:10.1007/s10994-016-5548-x