Pré-Publication, Document De Travail Année : 2025

Bilevel gradient methods and Morse parametric qualification

Résumé

Morse parametric qualification condition is a new condition that generalizes uniform strong convexity. Generic semi-algebraic functions are Morse parametric in a piecewise sense, implying that generic semi-algebraic bilevel problems reduce to mixed-integer programming. In this new framework, we study bilevel gradient algorithms with two strategies: the single-step multi-step strategy, which involves a sequence of steps on the lower-level problems followed by one step on the upper-level problem, and a differentiable programming strategy that optimizes a smooth approximation of the bilevel problem. While the first is shown to be a biased gradient method on the problem with rich properties, the second, inspired by meta-learning applications, is less stable but offers simplicity and ease of implementation.
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Dates et versions

hal-04942322 , version 1 (12-02-2025)

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  • HAL Id : hal-04942322 , version 1

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Jérôme Bolte, Quoc-Tung Le, Edouard Pauwels, Samuel Vaiter. Bilevel gradient methods and Morse parametric qualification. 2025. ⟨hal-04942322⟩
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