Trust-region algorithms: probabilistic complexity and intrinsic noise with applications to subsampling techniques

Stefania Bellavia, Gianmarco Gurioli, Benedetta Morini, Philippe TOINT

Résultats de recherche: Papier de travailArticle de travail

Résumé

A trust-region algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown that, under suitable probabilistic assumptions, the new method finds (in expectation) an epsilon-approximate minimizer of arbitrary order q>0in at most O(epsilon^{-(q+1)}) inexact evaluations of the function and its derivatives, providing the first such result for general optimality orders. The impact of intrinsic noise limiting the validity of the assumptions is also discussed and it is shown that difficulties are unlikely to occur in the first-order version of the algorithm for sufficiently large gradients. Conversely, should these assumptions fail for specific realizations, then ``degraded'' optimality guarantees are shown to hold when failure occurs. These conclusions are then discussed and illustrated in the context of subsampling methods for finite-sum optimization.
langue originaleAnglais
ÉditeurArxiv
Volume2112.06176
Etat de la publicationPublié - 2021

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