A non-monotone trust-region method with noisy oracles and additional sampling

Nataša Krejić (), Nataša Krklec Jerinkić (), Ángeles Martínez () and Mahsa Yousefi ()
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Nataša Krejić: University of Novi Sad
Nataša Krklec Jerinkić: University of Novi Sad
Ángeles Martínez: University of Trieste
Mahsa Yousefi: University of Florence

Computational Optimization and Applications, 2024, vol. 89, issue 1, No 8, 247-278

Abstract: Abstract In this work, we introduce a novel stochastic second-order method, within the framework of a non-monotone trust-region approach, for solving the unconstrained, nonlinear, and non-convex optimization problems arising in the training of deep neural networks. The proposed algorithm makes use of subsampling strategies that yield noisy approximations of the finite sum objective function and its gradient. We introduce an adaptive sample size strategy based on inexpensive additional sampling to control the resulting approximation error. Depending on the estimated progress of the algorithm, this can yield sample size scenarios ranging from mini-batch to full sample functions. We provide convergence analysis for all possible scenarios and show that the proposed method achieves almost sure convergence under standard assumptions for the trust-region framework. We report numerical experiments showing that the proposed algorithm outperforms its state-of-the-art counterpart in deep neural network training for image classification and regression tasks while requiring a significantly smaller number of gradient evaluations.

Keywords: Stochastic optimization; Second-order methods; Non-monotone trust-region; Quasi-Newton; Deep neural networks training; Adaptive sampling; 90C30; 90C06; 90C53; 90C90; 65K05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-024-00580-w

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