Imperial College London
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ProfessorDanCrisan

Faculty of Natural Sciences, Department of Mathematics

Professor of Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8489d.crisan Website

 
 
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Location

 

670Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Akyildiz:2020:10.1007/s11222-020-09964-4,
author = {Akyildiz, ÖD and Crisan, D and Míguez, J},
doi = {10.1007/s11222-020-09964-4},
journal = {Statistics and Computing},
pages = {1645--1663},
title = {Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization},
url = {http://dx.doi.org/10.1007/s11222-020-09964-4},
volume = {30},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed scheme is a stochastic zeroth-order optimization algorithm which demands only the capability to evaluate small subsets of components of the cost function. It can be depicted as a bank of samplers that generate particle approximations of several sequences of probability measures. These measures are constructed in such a way that they have associated probability density functions whose global maxima coincide with the global minima of the original cost function. The algorithm selects the best performing sampler and uses it to approximate a global minimum of the cost function. We prove analytically that the resulting estimator converges to a global minimum of the cost function almost surely and provide explicit convergence rates in terms of the number of generated Monte Carlo samples and the dimension of the search space. We show, by way of numerical examples, that the algorithm can tackle cost functions with multiple minima or with broad “flat” regions which are hard to minimize using gradient-based techniques.
AU  - Akyildiz,ÖD
AU  - Crisan,D
AU  - Míguez,J
DO  - 10.1007/s11222-020-09964-4
EP  - 1663
PY  - 2020///
SN  - 0960-3174
SP  - 1645
TI  - Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization
T2  - Statistics and Computing
UR  - http://dx.doi.org/10.1007/s11222-020-09964-4
UR  - https://link.springer.com/article/10.1007%2Fs11222-020-09964-4
UR  - http://hdl.handle.net/10044/1/82481
VL  - 30
ER  -
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