Réunion

Bilevel Optimization and Hyperparameter Learning

Annonce

Les demandes de prise en charge de missions seront traitées à partir du 27 janvier.

Bilevel optimization has become a crucial framework in machine learning for addressing hierarchical problems, where one optimization task depends on the outcome of another. This approach plays a pivotal role in hyperparameter learning, meta-learning, domain adaptation, and advanced regularization techniques.

The event will highlight recent developments in bilevel optimization and hyperparameter learning, exploring their theoretical foundations, numerical strategies, and diverse applications across machine learning and related fields. Topics of interest include (but are not limited to):

• Advances in bilevel optimization theory (convergence, complexity, and stability)
• Algorithms for solving bilevel problems efficiently
• Meta-learning, domain adaptation and transfer learning using bilevel frameworks
• Hyperparameter optimization and automated model selection
• Regularization and sparsity-inducing techniques in hyperparameter learning
• Applications to neural architecture search and optimization pipelines
• Robust hyperparameter learning for adversarial and noisy environments

This event, hosted at the École normale supérieure de Lyon (Site Monod, Room Condorcet) on March 25, 2025, invites contributions showcasing fundamental research, novel algorithms, or innovative applications that leverage bilevel optimization and hyperparameter learning for advancing the state of the art in machine learning.

Keynote Speakers:

• Luce BROTCORNE (Researcher, Inria)
  Introduction to Bilevel Optimization and Applications in Pricing
  (TBC)
• Julien MAIRAL (Researcher, Inria)
  Functional Bilevel Optimization for Machine Learning
  In this talk, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods developed in the parametric setting, where the inner objective is strongly convex with respect to the parameters of the prediction function. The functional point of view does not rely on this assumption and notably allows using over-parameterized neural networks as the inner prediction function. We propose scalable and efficient algorithms for the functional bilevel optimization problem and illustrate the benefits of our approach on instrumental regression and reinforcement learning tasks. This is a joint work with Ieva Petrulionyte and Michael Arbel.
• Saverio SALZO (Associate Professor, Sapienza Università di Roma)
  Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates
  I will address the problem of efficiently computing a generalized derivative of the fixed-point of a parametric nondifferentiable contraction map. This problem has wide applications in machine learning, including hyperparameter optimization, meta-learning and data poisoning attacks. Two popular approaches are analyzed: iterative differentiation (ITD) and approximate implicit differentiation (AID). A key challenge behind the nonsmooth setting is that the chain rule does not hold anymore. Building upon the recent work by Bolte et al. (2022), who proved linear convergence of nondifferentiable ITD, I will show an improved linear rate for ITD and a slightly better rate for AID, both in the deterministic case. I will also introduce NSID, a new stochastic method to compute the implicit derivative when the fixed point is defined as the composition of an outer map and an inner map which is accessible only through a stochastic unbiased estimator. Rates for such stochastic method rates will be presented.
• Antonio SILVETI-FALLS (Associate Professor, CVN, CentraleSupélec)
  Nonsmooth Implicit Differentiation for Machine Learning
  In view of training increasingly complex learning architectures, we establish a nonsmooth implicit function theorem with an operational calculus. Our result applies to most practical problems (i.e., definable problems) provided that a nonsmooth form of the classical invertibility condition is fulfilled. This approach allows for formal subdifferentiation: for instance, replacing derivatives by Clarke Jacobians in the usual differentiation formulas is fully justified for a wide class of nonsmooth problems. Moreover this calculus is entirely compatible with algorithmic differentiation (e.g., backpropagation). We provide several applications such as training deep equilibrium networks, training neural nets with conic optimization layers, or hyperparameter-tuning for nonsmooth Lasso-type models. To show the sharpness of our assumptions, we present numerical experiments showcasing the extremely pathological gradient dynamics one can encounter when applying implicit algorithmic differentiation without any hypothesis.
• Samuel VAITER (Researcher, CNRS, LJAD, Université Côte d’Azur)
  Successes and pitfalls of bilevel optimization in machine learning
  In this talk, I will introduce bilevel optimization (BO) as a powerful framework to address several machine learning-related problems, including hyperparameter tuning, meta-learning, and data cleaning. Based on this formulation, I will describe some successes of BO, particularly in a strongly convex setting, where strong guarantees can be provided along with efficient stochastic algorithms. I will also discuss the outstanding issues of this framework, presenting geometrical and computational complexity results that show the potential difficulties in going beyond convexity, at least from a theoretical perspective.

Call: Those wishing to present their work are invited to express their intent to the organizers before 04/03/2025 by emailing the organizers with a title, an abstract, and the list of authors, using the subject « GDR IASIS Bilevel, » at the following addresses: jordan.frecon-deloire@inria.fr, quentin.bertrand@inria.fr, mathurin.massias@inria.fr.

Organizing Team:

• Jordan FRECON PATRACONE (Associate Professor, Inria, LabHC)
• Quentin BERTRAND (Researcher, Inria, LabHC)
• Mathurin MASSIAS (Researcher, Inria, LIP)