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Gradient Estimation Schemes for Noisy Functions

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  • Brekelmans, R.C.M.

    (Tilburg University, School of Economics and Management)

  • Driessen, L.
  • Hamers, H.J.M.

    (Tilburg University, School of Economics and Management)

  • den Hertog, D.

    (Tilburg University, School of Economics and Management)

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.
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Suggested Citation

  • Brekelmans, R.C.M. & Driessen, L. & Hamers, H.J.M. & den Hertog, D., 2003. "Gradient Estimation Schemes for Noisy Functions," Other publications TiSEM 4aa4fd63-80d9-4989-89a8-0, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:4aa4fd63-80d9-4989-89a8-0c1683fc5c4f
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    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.
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    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.

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