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Amortized implicit differentiation for stochastic bilevel optimization

Michael Arbel 1 Julien Mairal 1 
1 Thoth - Apprentissage de modèles à partir de données massives
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann
Abstract : We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit differentiation and we exploit a warm-start strategy to amortize the estimation of the exact gradient. We then introduce a unified theoretical framework inspired by the study of singularly perturbed systems (Habets, 1974) to analyze such amortized algorithms. By using this framework, our analysis shows these algorithms to match the computational complexity of oracle methods that have access to an unbiased estimate of the gradient, thus outperforming many existing results for bilevel optimization. We illustrate these findings on synthetic experiments and demonstrate the efficiency of these algorithms on hyper-parameter optimization experiments involving several thousands of variables.
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https://hal.archives-ouvertes.fr/hal-03455458
Contributor : Michael Arbel Connect in order to contact the contributor
Submitted on : Monday, November 29, 2021 - 4:28:41 PM
Last modification on : Friday, February 4, 2022 - 3:21:12 AM

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Michael Arbel, Julien Mairal. Amortized implicit differentiation for stochastic bilevel optimization. The Tenth International Conference on Learning Representations, Apr 2022, Online, France. ⟨hal-03455458⟩

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