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Asymptotic bias of stochastic gradient search

Abstract:
The asymptotic behavior of the stochastic gradient algorithm using biased gradient estimates is analyzed. Relying on arguments based on dynamic system theory (chain-recurrence) and differential geometry (Yomdin theorem and Lojasiewicz inequalities), upper bounds on the asymptotic bias of this algorithm are derived. The results hold under mild conditions and cover a broad class of algorithms used in machine learning, signal processing and statistics.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Publisher copy:
10.1214/16-AAP1272

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Department:
Hertford College
Role:
Author
Publisher:
Institute of Mathematical Statistics Publisher's website
Journal:
Annals of Applied Probability Journal website
Volume:
27
Issue:
6
Pages:
3255-3304
Publication date:
2017-12-05
Acceptance date:
2016-12-24
DOI:
EISSN:
2168-8737
ISSN:
1050-5164
Pubs id:
pubs:679242
URN:
uri:f9cba224-fdae-4c38-892f-946443441dca
UUID:
uuid:f9cba224-fdae-4c38-892f-946443441dca
Local pid:
pubs:679242

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