Imperial College London
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Professor Grigorios A. Pavliotis

Faculty of Natural Sciences, Department of Mathematics

Professor of Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8564g.pavliotis Website

 
 
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Location

 

736aHuxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Borovykh:2021:10.1016/j.physd.2021.132844,
author = {Borovykh, A and Kantas, N and Parpas, P and Pavliotis, GA},
doi = {10.1016/j.physd.2021.132844},
journal = {Physica D: Nonlinear Phenomena},
pages = {1--21},
title = {On stochastic mirror descent with interacting particles: Convergence properties and variance reduction},
url = {http://dx.doi.org/10.1016/j.physd.2021.132844},
volume = {418},
year = {2021}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - An open problem in optimization with noisy information is the computation of an exact minimizer that is independent of the amount of noise. A standard practice in stochastic approximation algorithms is to use a decreasing step-size. This however leads to a slower convergence. A second alternative is to use a fixed step-size and run independent replicas of the algorithm and average these. A third option is to run replicas of the algorithm and allow them to interact. It is unclear which of these options works best. To address this question, we reduce the problem of the computation of an exact minimizer with noisy gradient information to the study of stochastic mirror descent with interacting particles. We study the convergence of stochastic mirror descent and make explicit the tradeoffs between communication and variance reduction. We provide theoretical and numerical evidence to suggest that interaction helps to improve convergence and reduce the variance of the estimate.
AU  - Borovykh,A
AU  - Kantas,N
AU  - Parpas,P
AU  - Pavliotis,GA
DO  - 10.1016/j.physd.2021.132844
EP  - 21
PY  - 2021///
SN  - 0167-2789
SP  - 1
TI  - On stochastic mirror descent with interacting particles: Convergence properties and variance reduction
T2  - Physica D: Nonlinear Phenomena
UR  - http://dx.doi.org/10.1016/j.physd.2021.132844
UR  - https://www.sciencedirect.com/science/article/pii/S0167278921000026?via%3Dihub
UR  - http://hdl.handle.net/10044/1/89025
VL  - 418
ER  -
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