Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911839949946880 |
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| author | Maier, Severin Castera, Camille Ochs, Peter |
| author_facet | Maier, Severin Castera, Camille Ochs, Peter |
| contents | We introduce an autonomous system with closed-loop damping for first-order convex optimization. While, to this day, optimal rates of convergence are almost exclusively achieved by non-autonomous methods via open-loop damping (e.g., Nesterov's algorithm), we show that our system, featuring a closed-loop damping, exhibits a rate arbitrarily close to the optimal one. We do so by coupling the damping and the speed of convergence of the system via a well-chosen Lyapunov function. By discretizing our system we then derive an algorithm and present numerical experiments supporting our theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_10053 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization Maier, Severin Castera, Camille Ochs, Peter Optimization and Control Machine Learning Dynamical Systems We introduce an autonomous system with closed-loop damping for first-order convex optimization. While, to this day, optimal rates of convergence are almost exclusively achieved by non-autonomous methods via open-loop damping (e.g., Nesterov's algorithm), we show that our system, featuring a closed-loop damping, exhibits a rate arbitrarily close to the optimal one. We do so by coupling the damping and the speed of convergence of the system via a well-chosen Lyapunov function. By discretizing our system we then derive an algorithm and present numerical experiments supporting our theoretical findings. |
| title | Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization |
| topic | Optimization and Control Machine Learning Dynamical Systems |
| url | https://arxiv.org/abs/2311.10053 |