We propose a stochastic first-order trust-region method with inexact function and gradient evaluations for solving finite-sum minimization problems. Using a suitable reformulation of the given problem, our method combines the inexact restoration approach for constrained optimization with the trust-region procedure and random models. Differently from other recent stochastic trust-region schemes, our proposed algorithm improves feasibility and optimality in a modular way. We provide the expected number of iterations for reaching a near-stationary point by imposing some probability accuracy requirements on random functions and gradients which are, in general, less stringent than the corresponding ones in literature. We validate the proposed algorithm on some nonconvex optimization problems arising in binary classification and regression, showing that it performs well in terms of cost and accuracy, and allows to reduce the burdensome tuning of the hyper-parameters involved.

A stochastic first-order trust-region method with inexact restoration for finite-sum minimization / Stefania Bellavia, Natasa Krejic, Benedetta Morini, Simone Rebegoldi. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 1573-2894. - STAMPA. - 84:(2023), pp. 53-84. [10.1007/s10589-022-00430-7]

A stochastic first-order trust-region method with inexact restoration for finite-sum minimization

Stefania Bellavia;Benedetta Morini
;
Simone Rebegoldi
2023

Abstract

We propose a stochastic first-order trust-region method with inexact function and gradient evaluations for solving finite-sum minimization problems. Using a suitable reformulation of the given problem, our method combines the inexact restoration approach for constrained optimization with the trust-region procedure and random models. Differently from other recent stochastic trust-region schemes, our proposed algorithm improves feasibility and optimality in a modular way. We provide the expected number of iterations for reaching a near-stationary point by imposing some probability accuracy requirements on random functions and gradients which are, in general, less stringent than the corresponding ones in literature. We validate the proposed algorithm on some nonconvex optimization problems arising in binary classification and regression, showing that it performs well in terms of cost and accuracy, and allows to reduce the burdensome tuning of the hyper-parameters involved.
2023
84
53
84
Stefania Bellavia, Natasa Krejic, Benedetta Morini, Simone Rebegoldi
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1286426
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