A systematic approach to Lyapunov analyses of continuous-time models in convex optimization
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866914709512388608 |
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| author | Moucer, Céline Taylor, Adrien Bach, Francis |
| author_facet | Moucer, Céline Taylor, Adrien Bach, Francis |
| contents | First-order methods are often analyzed via their continuous-time models, where their worst-case convergence properties are usually approached via Lyapunov functions. In this work, we provide a systematic and principled approach to find and verify Lyapunov functions for classes of ordinary and stochastic differential equations. More precisely, we extend the performance estimation framework, originally proposed by Drori and Teboulle [10], to continuous-time models. We retrieve convergence results comparable to those of discrete methods using fewer assumptions and convexity inequalities, and provide new results for stochastic accelerated gradient flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_12772 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A systematic approach to Lyapunov analyses of continuous-time models in convex optimization Moucer, Céline Taylor, Adrien Bach, Francis Numerical Analysis First-order methods are often analyzed via their continuous-time models, where their worst-case convergence properties are usually approached via Lyapunov functions. In this work, we provide a systematic and principled approach to find and verify Lyapunov functions for classes of ordinary and stochastic differential equations. More precisely, we extend the performance estimation framework, originally proposed by Drori and Teboulle [10], to continuous-time models. We retrieve convergence results comparable to those of discrete methods using fewer assumptions and convexity inequalities, and provide new results for stochastic accelerated gradient flows. |
| title | A systematic approach to Lyapunov analyses of continuous-time models in convex optimization |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2205.12772 |