Stochastic derivative-free optimization using a trust region framework
Abstract
This study presents a trust region algorithm to minimize a function f when one has access only to noise-corrupted function values f¯. The model-based algorithm dynamically adjusts its step length, taking larger steps when the model and function agree and smaller steps when the model is less accurate. The method does not require the user to specify a fixed pattern of points used to build local models and does not repeatedly sample points. If f is sufficiently smooth and the noise is independent and identically distributed with mean zero and finite variance, we prove that our algorithm produces iterates such that the corresponding function gradients converge in probability to zero. As a result, we present a prototype of our algorithm that, while simplistic in its management of previously evaluated points, solves benchmark problems in fewer function evaluations than do existing stochastic approximation methods.
- Authors:
-
- Argonne National Lab. (ANL), Lemont, IL (United States)
- Univ. of Colorado, Denver, CO (United States)
- Publication Date:
- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
- OSTI Identifier:
- 1366470
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Computational Optimization and applications
- Additional Journal Information:
- Journal Volume: 64; Journal Issue: 3; Journal ID: ISSN 0926-6003
- Publisher:
- Springer
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; derivative-free optimization; model-based trust region methods; stochastic optimization
Citation Formats
Larson, Jeffrey, and Billups, Stephen C. Stochastic derivative-free optimization using a trust region framework. United States: N. p., 2016.
Web. doi:10.1007/s10589-016-9827-z.
Larson, Jeffrey, & Billups, Stephen C. Stochastic derivative-free optimization using a trust region framework. United States. doi:10.1007/s10589-016-9827-z.
Larson, Jeffrey, and Billups, Stephen C. Wed .
"Stochastic derivative-free optimization using a trust region framework". United States. doi:10.1007/s10589-016-9827-z. https://www.osti.gov/servlets/purl/1366470.
@article{osti_1366470,
title = {Stochastic derivative-free optimization using a trust region framework},
author = {Larson, Jeffrey and Billups, Stephen C.},
abstractNote = {This study presents a trust region algorithm to minimize a function f when one has access only to noise-corrupted function values f¯. The model-based algorithm dynamically adjusts its step length, taking larger steps when the model and function agree and smaller steps when the model is less accurate. The method does not require the user to specify a fixed pattern of points used to build local models and does not repeatedly sample points. If f is sufficiently smooth and the noise is independent and identically distributed with mean zero and finite variance, we prove that our algorithm produces iterates such that the corresponding function gradients converge in probability to zero. As a result, we present a prototype of our algorithm that, while simplistic in its management of previously evaluated points, solves benchmark problems in fewer function evaluations than do existing stochastic approximation methods.},
doi = {10.1007/s10589-016-9827-z},
journal = {Computational Optimization and applications},
number = 3,
volume = 64,
place = {United States},
year = {2016},
month = {2}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Estimating Derivatives of Noisy Simulations
journal, April 2012
- Moré, Jorge J.; Wild, Stefan M.
- ACM Transactions on Mathematical Software, Vol. 38, Issue 3
UOBYQA: unconstrained optimization by quadratic approximation
journal, May 2002
- Powell, M. J. D.
- Mathematical Programming, Vol. 92, Issue 3
Stochastic Trust-Region Response-Surface Method (STRONG)—A New Response-Surface Framework for Simulation Optimization
journal, May 2013
- Chang, Kuo-Hao; Hong, L. Jeff; Wan, Hong
- INFORMS Journal on Computing, Vol. 25, Issue 2
Lipschitzian optimization without the Lipschitz constant
journal, October 1993
- Jones, D. R.; Perttunen, C. D.; Stuckman, B. E.
- Journal of Optimization Theory and Applications, Vol. 79, Issue 1
Derivative-Free Optimization of Expensive Functions with Computational Error Using Weighted Regression
journal, January 2013
- Billups, Stephen C.; Larson, Jeffrey; Graf, Peter
- SIAM Journal on Optimization, Vol. 23, Issue 1
A Simplex Method for Function Minimization
journal, January 1965
- Nelder, J. A.; Mead, R.
- The Computer Journal, Vol. 7, Issue 4
Multivariate stochastic approximation using a simultaneous perturbation gradient approximation
journal, March 1992
- Spall, J. C.
- IEEE Transactions on Automatic Control, Vol. 37, Issue 3
Estimating Computational Noise
journal, January 2011
- Moré, Jorge J.; Wild, Stefan M.
- SIAM Journal on Scientific Computing, Vol. 33, Issue 3
Benchmarking Derivative-Free Optimization Algorithms
journal, January 2009
- Moré, Jorge J.; Wild, Stefan M.
- SIAM Journal on Optimization, Vol. 20, Issue 1
Stochastic Estimation of the Maximum of a Regression Function
journal, September 1952
- Kiefer, J.; Wolfowitz, J.
- The Annals of Mathematical Statistics, Vol. 23, Issue 3
Benchmarking optimization software with performance profiles
journal, January 2002
- Dolan, Elizabeth D.; Moré, Jorge J.
- Mathematical Programming, Vol. 91, Issue 2
Convergence of Trust-Region Methods Based on Probabilistic Models
journal, January 2014
- Bandeira, A. S.; Scheinberg, K.; Vicente, L. N.
- SIAM Journal on Optimization, Vol. 24, Issue 3