Camille Castera (University of Tübingen)
| Quand ? |
Le 21/11/2023, de 13:00 à 14:00 |
|---|---|
| Où ? | M7 101 |
| Participants |
Camille Castera |
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Speaker: Camille Castera
https://scholar.google.fr/citations?user=FjQAMMUAAAAJ&hl=fr
Title: Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization
Abstract: Nesterov's algorithm remains mysterious in many ways, such as its intriguing so-called damping coefficient $(k-1)/(k+2)$, crucial for its efficiency. This coefficient is said to be ""open-loop" as it depends on the iteration index $k$, making the initial iteration index an hyper-parameter that affects the performance of the method (unlike most other popular algorithms). To overcome this issue, we introduce a new continuous-time system with "closed-loop" damping. We do so by replacing the open-loop coefficient by the square root of a Lyapunov function, hence coupling the damping with the speed of convergence of the system. We show that our system is the first closed-loop strategy that achieves a convergence rate arbitrarily close to the optimal one for first-order methods on smooth convex functions. We then derive a practical first-order algorithm, via explicit discretization of the system and present numerical experiments supporting our theoretical findings. This is joint work with S. Maier and P. Ochs.
In Room M7 101