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A framework for bilevel optimization that enables stochastic and global variance reduction algorithms

26 Maggio 2022 alle Ore: 16:30

Luogo: Aula 5016 (Lab LM).

Speaker: Pierre Ablin (CNRS & Université Paris-Dauphine)

Persona di riferimento: Pierre Laforgue

Abstract

Bilevel optimization, the problem of minimizing a value function which involves the arg-minimum of another function,  appears in many areas of machine learning. In a large-scale setting where the number of samples is huge, it is crucial to develop stochastic methods, which only use a few samples at a time to progress. However, computing the gradient of the value function involves solving a linear system, which makes it difficult to derive unbiased stochastic estimates. To overcome this problem we introduce a novel framework, in which the solution of the inner problem, the solution of the linear system, and the main variable evolve at the same time. These directions are written as a sum, making it straightforward to derive unbiased estimates. The simplicity of our approach allows us to develop global variance reduction algorithms, where the dynamics of all variables is subject to variance reduction. We demonstrate that SABA, an adaptation of the celebrated SAGA algorithm in our framework, has O(1/T)  convergence rate, and that it achieves linear convergence under Polyak-Lojasciewicz assumption. This is the first stochastic algorithm for bilevel optimization that verifies either of these properties. Numerical experiments validate the usefulness of our method. Reference: M.Dagréou, P.Ablin, S.Vaiter and T.Moreau. "A framework for bilevel optimization that enables stochastic and global variance reduction algorithms". https://arxiv.org/abs/2201.13409

Bio sketch

Pierre Ablin is a research scientist at CNRS and Université Paris-Dauphine. His research focuses on different areas of machine learning: the development of fast optimization algorithms, practical and theoretical links between neural networks and other domains like optimization and control theory, learning under geometrical constraints, and the application of machine learning methods to brain signal processing. Prior to joining CNRS, he was a postdoc at Ecole Normale Supérieure in Paris, working with Gabriel Peyré on practical and theoretical deep learning. Pierre received the
Master's degree from École polytechnique in France and Imperia College London. He received his Ph.D. from Inria, under the supervision of Alexandre Gramfort and Jean-François Cardoso, where he developed faster and more expressive unsupervised algorithms for brain signal processing.

04 maggio 2022
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