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Stochastic average model methods

Author

Listed:
  • Matt Menickelly

    (Argonne National Laboratory)

  • Stefan M. Wild

    (Argonne National Laboratory
    Lawrence Berkeley National Laboratory)

Abstract

We consider the solution of finite-sum minimization problems, such as those appearing in nonlinear least-squares or general empirical risk minimization problems. We are motivated by problems in which the summand functions are computationally expensive and evaluating all summands on every iteration of an optimization method may be undesirable. We present the idea of stochastic average model (SAM) methods, inspired by stochastic average gradient methods. SAM methods sample component functions on each iteration of a trust-region method according to a discrete probability distribution on component functions; the distribution is designed to minimize an upper bound on the variance of the resulting stochastic model. We present promising numerical results concerning an implemented variant extending the derivative-free model-based trust-region solver POUNDERS, which we name SAM-POUNDERS.

Suggested Citation

  • Matt Menickelly & Stefan M. Wild, 2024. "Stochastic average model methods," Computational Optimization and Applications, Springer, vol. 88(2), pages 405-442, June.
    • Handle: RePEc:spr:coopap:v:88:y:2024:i:2:d:10.1007_s10589-024-00563-x
    DOI: 10.1007/s10589-024-00563-x
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    References listed on IDEAS

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    1. Nibia Aires, 1999. "Algorithms to Find Exact Inclusion Probabilities for Conditional Poisson Sampling and Pareto πps Sampling Designs," Methodology and Computing in Applied Probability, Springer, vol. 1(4), pages 457-469, December.
    2. Chen, Sean X., 2000. "General Properties and Estimation of Conditional Bernoulli Models," Journal of Multivariate Analysis, Elsevier, vol. 74(1), pages 69-87, July.
    3. Hongchao Zhang & Andrew Conn, 2012. "On the local convergence of a derivative-free algorithm for least-squares minimization," Computational Optimization and Applications, Springer, vol. 51(2), pages 481-507, March.
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