Long term dynamics of the subgradient method for Lipschitz path differentiable functions - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage Access content directly
Journal Articles Journal of the European Mathematical Society Year : 2022

Long term dynamics of the subgradient method for Lipschitz path differentiable functions

Abstract

We consider the long-term dynamics of the vanishing stepsize subgradient method in the case when the objective function is neither smooth nor convex. We assume that this function is locally Lipschitz and path differentiable, i.e., admits a chain rule. Our study departs from other works in the sense that we focus on the behavoir of the oscillations, and to do this we use closed measures. We recover known convergence results, establish new ones, and show a local principle of oscillation compensation for the velocities. Roughly speaking, the time average of gradients around one limit point vanishes. This allows us to further analyze the structure of oscillations, and establish their perpendicularity to the general drift.
Fichier principal
Vignette du fichier
Oscillation_compensation.pdf (532.98 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03614899 , version 1 (24-01-2023)

Identifiers

Cite

Jérôme Bolte, Edouard Pauwels, Rodolfo Ríos-Zertuche. Long term dynamics of the subgradient method for Lipschitz path differentiable functions. Journal of the European Mathematical Society, 2022, pp.1-28. ⟨10.4171/JEMS/1285⟩. ⟨hal-03614899⟩
106 View
57 Download

Altmetric

Share

Gmail Facebook X LinkedIn More