IDEAS home Printed from https://ideas.repec.org/p/tiu/tiucen/4aa4fd63-80d9-4989-89a8-0c1683fc5c4f.html
   My bibliography  Save this paper

Gradient Estimation Schemes for Noisy Functions

Author

Listed:
  • Brekelmans, R.C.M.

    (Tilburg University, Center For Economic Research)

  • Driessen, L.
  • Hamers, H.J.M.

    (Tilburg University, Center For Economic Research)

  • den Hertog, D.

    (Tilburg University, Center For Economic Research)

Abstract

In this paper, we analyze different schemes for obtaining gradient estimates when the underlying functions are noisy. Good gradient estimation is important e.g. for nonlinear programming solvers. As error criterion, we take the norm of the difference between the real and estimated gradients. The total error can be split into a deterministic error and a stochastic error. For three finite-difference schemes and two design of experiments (DoE) schemes, we analyze both the deterministic errors and stochastic errors. We derive also optimal stepsizes for each scheme, such that the total error is minimized. Some of the schemes have the nice property that this stepsize minimizes also the variance of the error. Based on these results, we show that, to obtain good gradient estimates for noisy functions, it is worthwhile to use DoE schemes. We recommend to implement such schemes in NLP solvers.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowe
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Brekelmans, R.C.M. & Driessen, L. & Hamers, H.J.M. & den Hertog, D., 2003. "Gradient Estimation Schemes for Noisy Functions," Discussion Paper 2003-12, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:4aa4fd63-80d9-4989-89a8-0c1683fc5c4f
    as

    Download full text from publisher

    File URL: https://pure.uvt.nl/ws/portalfiles/portal/544749/12.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Michael A. Zazanis & Rajan Suri, 1993. "Convergence Rates of Finite-Difference Sensitivity Estimates for Stochastic Systems," Operations Research, INFORMS, vol. 41(4), pages 694-703, August.
    2. Joan M. Donohue & Ernest C. Houck & Raymond H. Myers, 1995. "Simulation Designs for the Estimation of Quadratic Response Surface Gradients in the Presence of Model Misspecification," Management Science, INFORMS, vol. 41(2), pages 244-262, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. R. C. M. Brekelmans & L. T. Driessen & H. J. M. Hamers & D. Hertog, 2008. "Gradient Estimation Using Lagrange Interpolation Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 341-357, March.
    2. Angun, M.E., 2004. "Black box simulation optimization : Generalized response surface methodology," Other publications TiSEM 2548e953-54ce-44e2-8c5b-7, Tilburg University, School of Economics and Management.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Angun, M.E. & Kleijnen, Jack P.C., 2012. "An asymptotic test of optimality conditions in multiresponse simulation optimization," Other publications TiSEM a69dfa59-b0e1-45bd-8cd6-a, Tilburg University, School of Economics and Management.
    2. Safizadeh, M. Hossein, 2002. "Minimizing the bias and variance of the gradient estimate in RSM simulation studies," European Journal of Operational Research, Elsevier, vol. 136(1), pages 121-135, January.
    3. Kleijnen, Jack P. C. & den Hertog, Dick & Angun, Ebru, 2004. "Response surface methodology's steepest ascent and step size revisited," European Journal of Operational Research, Elsevier, vol. 159(1), pages 121-131, November.
    4. Ebru Angün & Jack Kleijnen, 2012. "An Asymptotic Test of Optimality Conditions in Multiresponse Simulation Optimization," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 53-65, February.
    5. Arsham H., 1998. "Techniques for Monte Carlo Optimizing," Monte Carlo Methods and Applications, De Gruyter, vol. 4(3), pages 181-230, December.
    6. Borgonovo, Emanuele & Rabitti, Giovanni, 2023. "Screening: From tornado diagrams to effective dimensions," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1200-1211.
    7. Angun, M.E., 2004. "Black box simulation optimization : Generalized response surface methodology," Other publications TiSEM 2548e953-54ce-44e2-8c5b-7, Tilburg University, School of Economics and Management.
    8. Batmaz, Inci & Tunali, Semra, 2003. "Small response surface designs for metamodel estimation," European Journal of Operational Research, Elsevier, vol. 145(2), pages 455-470, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tiu:tiucen:4aa4fd63-80d9-4989-89a8-0c1683fc5c4f. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Richard Broekman (email available below). General contact details of provider: http://center.uvt.nl .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.