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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Published in | Machine learning Vol. 104; no. 1; pp. 129 - 148 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
New York
Springer US
01.07.2016
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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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. |
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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 0885-6125 1573-0565 |
DOI: | 10.1007/s10994-016-5548-x |