Stochastic Gradient Methods with Preconditioned Updates
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913278616141824 |
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| author | Sadiev, Abdurakhmon Beznosikov, Aleksandr Almansoori, Abdulla Jasem Kamzolov, Dmitry Tappenden, Rachael Takáč, Martin |
| author_facet | Sadiev, Abdurakhmon Beznosikov, Aleksandr Almansoori, Abdulla Jasem Kamzolov, Dmitry Tappenden, Rachael Takáč, Martin |
| contents | This work considers the non-convex finite sum minimization problem. There are several algorithms for such problems, but existing methods often work poorly when the problem is badly scaled and/or ill-conditioned, and a primary goal of this work is to introduce methods that alleviate this issue. Thus, here we include a preconditioner based on Hutchinson's approach to approximating the diagonal of the Hessian, and couple it with several gradient-based methods to give new scaled algorithms: Scaled SARAH and Scaled L-SVRG. Theoretical complexity guarantees under smoothness assumptions are presented. We prove linear convergence when both smoothness and the PL condition are assumed. Our adaptively scaled methods use approximate partial second-order curvature information and, therefore, can better mitigate the impact of badly scaled problems. This improved practical performance is demonstrated in the numerical experiments also presented in this work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_00285 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stochastic Gradient Methods with Preconditioned Updates Sadiev, Abdurakhmon Beznosikov, Aleksandr Almansoori, Abdulla Jasem Kamzolov, Dmitry Tappenden, Rachael Takáč, Martin Optimization and Control Machine Learning This work considers the non-convex finite sum minimization problem. There are several algorithms for such problems, but existing methods often work poorly when the problem is badly scaled and/or ill-conditioned, and a primary goal of this work is to introduce methods that alleviate this issue. Thus, here we include a preconditioner based on Hutchinson's approach to approximating the diagonal of the Hessian, and couple it with several gradient-based methods to give new scaled algorithms: Scaled SARAH and Scaled L-SVRG. Theoretical complexity guarantees under smoothness assumptions are presented. We prove linear convergence when both smoothness and the PL condition are assumed. Our adaptively scaled methods use approximate partial second-order curvature information and, therefore, can better mitigate the impact of badly scaled problems. This improved practical performance is demonstrated in the numerical experiments also presented in this work. |
| title | Stochastic Gradient Methods with Preconditioned Updates |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2206.00285 |