A non-monotone trust-region method with noisy oracles and additional sampling
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 subsamp...
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| Published in: | Computational optimization and applications Vol. 89; no. 1; pp. 247 - 278 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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01.09.2024
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| ISSN: | 0926-6003, 1573-2894 |
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| 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. |
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| AbstractList | 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. |
| Author | Yousefi, Mahsa Krklec Jerinkić, Nataša Krejić, Nataša Martínez, Ángeles |
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| CitedBy_id | crossref_primary_10_1007_s10589_025_00664_1 crossref_primary_10_1007_s10589_025_00720_w crossref_primary_10_1016_j_cam_2025_117059 |
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| Keywords | 90C53 90C30 65K05 Adaptive sampling Second-order methods Deep neural networks training 90C06 90C90 Stochastic optimization Non-monotone trust-region Quasi-Newton |
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