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Pré-Publication, Document De Travail Année : 2024

Inexact subgradient methods for semialgebraic functions

Résumé

Motivated by the widespread use of approximate derivatives in machine learning and optimization, we study inexact subgradient methods with non-vanishing additive errors and step sizes. In the nonconvex semialgebraic setting, under boundedness assumptions, we prove that the method provides points that eventually fluctuate close to the critical set at a distance proportional to $\epsilon^\rho$ where $\epsilon$ is the error in subgradient evaluation and $\rho$ relates to the geometry of the problem. In the convex setting, we provide complexity results for the averaged values. We also obtain byproducts of independent interest, such as descent-like lemmas for nonsmooth nonconvex problems and some results on the limit of affine interpolants of differential inclusions.
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Dates et versions

hal-04562371 , version 1 (29-04-2024)

Identifiants

  • HAL Id : hal-04562371 , version 1

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Jérôme Bolte, Tam Le, Éric Moulines, Edouard Pauwels. Inexact subgradient methods for semialgebraic functions. 2024. ⟨hal-04562371⟩
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