Projected Forward Gradient-Guided Frank-Wolfe Algorithm via Variance Reduction
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909440605683712 |
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| author | Rostami, M. Kia, S. S. |
| author_facet | Rostami, M. Kia, S. S. |
| contents | This paper aims to enhance the use of the Frank-Wolfe (FW) algorithm for training deep neural networks. Similar to any gradient-based optimization algorithm, FW suffers from high computational and memory costs when computing gradients for DNNs. This paper introduces the application of the recently proposed projected forward gradient (Projected-FG) method to the FW framework, offering reduced computational cost similar to backpropagation and low memory utilization akin to forward propagation. Our results show that trivial application of the Projected-FG introduces non-vanishing convergence error due to the stochastic noise that the Projected-FG method introduces in the process. This noise results in an non-vanishing variance in the Projected-FG estimated gradient. To address this, we propose a variance reduction approach by aggregating historical Projected-FG directions. We demonstrate rigorously that this approach ensures convergence to the optimal solution for convex functions and to a stationary point for non-convex functions. These convergence properties are validated through a numerical example, showcasing the approach's effectiveness and efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12511 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Projected Forward Gradient-Guided Frank-Wolfe Algorithm via Variance Reduction Rostami, M. Kia, S. S. Machine Learning Optimization and Control This paper aims to enhance the use of the Frank-Wolfe (FW) algorithm for training deep neural networks. Similar to any gradient-based optimization algorithm, FW suffers from high computational and memory costs when computing gradients for DNNs. This paper introduces the application of the recently proposed projected forward gradient (Projected-FG) method to the FW framework, offering reduced computational cost similar to backpropagation and low memory utilization akin to forward propagation. Our results show that trivial application of the Projected-FG introduces non-vanishing convergence error due to the stochastic noise that the Projected-FG method introduces in the process. This noise results in an non-vanishing variance in the Projected-FG estimated gradient. To address this, we propose a variance reduction approach by aggregating historical Projected-FG directions. We demonstrate rigorously that this approach ensures convergence to the optimal solution for convex functions and to a stationary point for non-convex functions. These convergence properties are validated through a numerical example, showcasing the approach's effectiveness and efficiency. |
| title | Projected Forward Gradient-Guided Frank-Wolfe Algorithm via Variance Reduction |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2403.12511 |