Stochastic average model methods

Matt Menickelly () and Stefan M. Wild ()
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Matt Menickelly: Argonne National Laboratory
Stefan M. Wild: Argonne National Laboratory

Computational Optimization and Applications, 2024, vol. 88, issue 2, No 1, 405-442

Abstract: 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.

Keywords: Finite-sum minimization; Data fitting; Optimization; Derivative-free optimization; Nonlinear optimization; Randomized methods (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-024-00563-x

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