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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.17100 |
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| _version_ | 1866916176380035072 |
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| author | Driggs, Derek Ehrhardt, Matthias J. Schönlieb, Carola-Bibiane Tang, Junqi |
| author_facet | Driggs, Derek Ehrhardt, Matthias J. Schönlieb, Carola-Bibiane Tang, Junqi |
| contents | The Condat-Vũ algorithm is a widely used primal-dual method for optimizing composite objectives of three functions. Several algorithms for optimizing composite objectives of two functions are special cases of Condat-Vũ, including proximal gradient descent (PGD). It is well-known that PGD exhibits suboptimal performance, and a simple adjustment to PGD can accelerate its convergence rate from $\mathcal{O}(1/T)$ to $\mathcal{O}(1/T^2)$ on convex objectives, and this accelerated rate is optimal. In this work, we show that a simple adjustment to the Condat-Vũ algorithm allows it to recover accelerated PGD (APGD) as a special case, instead of PGD. We prove that this accelerated Condat--Vũ algorithm achieves optimal convergence rates and significantly outperforms the traditional Condat-Vũ algorithm in regimes where the Condat--Vũ algorithm approximates the dynamics of PGD. We demonstrate the effectiveness of our approach in various applications in machine learning and computational imaging. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17100 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Practical Acceleration of the Condat-Vũ Algorithm Driggs, Derek Ehrhardt, Matthias J. Schönlieb, Carola-Bibiane Tang, Junqi Optimization and Control The Condat-Vũ algorithm is a widely used primal-dual method for optimizing composite objectives of three functions. Several algorithms for optimizing composite objectives of two functions are special cases of Condat-Vũ, including proximal gradient descent (PGD). It is well-known that PGD exhibits suboptimal performance, and a simple adjustment to PGD can accelerate its convergence rate from $\mathcal{O}(1/T)$ to $\mathcal{O}(1/T^2)$ on convex objectives, and this accelerated rate is optimal. In this work, we show that a simple adjustment to the Condat-Vũ algorithm allows it to recover accelerated PGD (APGD) as a special case, instead of PGD. We prove that this accelerated Condat--Vũ algorithm achieves optimal convergence rates and significantly outperforms the traditional Condat-Vũ algorithm in regimes where the Condat--Vũ algorithm approximates the dynamics of PGD. We demonstrate the effectiveness of our approach in various applications in machine learning and computational imaging. |
| title | Practical Acceleration of the Condat-Vũ Algorithm |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2403.17100 |