SPOT

Prochains exposés

SPOT 106 – Lundi 4 mai 2026 – Salle des thèses (C002) à l’ENSEEIHT (N7), 2 rue Charles Camichel, 31000 Toulouse

14h – Anas Bouali (Montpellier) – Regularization of optimal control problems on stratified domains using additional controls

In this presentation, we investigate a Mayer optimal control problem governed by a dynamics defined regionally.
We consider that the state space is stratified into a family of disjoint regions with nonsmooth interfaces, and that in each region, the dynamics is given by a smooth expression as follows: $ \dot{x} = f_j(x, u)$  if $\varphi_j(x) < 0 $.
First, it is shown that this problem is equivalent to a new optimal control problem, with additional controls $v_j$ taking values in $[0, 1]$ and a (smooth) dynamics as a convex combination of the smooth dynamics $\sum_{j=1}^{N} v_j f_j(x, u_j)$ along with the following mixed control-state constraint: $(1 – 2v_j) \varphi_j(x) = |\varphi_j(x)|$.
Next, we introduce a family of auxiliary optimal control problems. In these problems, we first regularize the nonsmooth interfaces. In addition, we consider the convex combination of smooth dynamics (only) within a boundary layer. Furthermore, we add a penalization term to the cost function to account for the mixed control-state constraint.
Our main result is that solutions to these (smooth) problems converge (up to a subsequence) to a solution of the original one. It is obtained thanks to a new hypothesis related to solutions to the auxiliary problems, which is weaker than the transverse crossing condition of the literature. This technique is implemented numerically on two examples involving non-transverse crossings of interfaces, showing its efficiency.

15h – Xiaoyi Mai (Toulouse) - Correcting Overparameterization Effects in Fair Empirical Risk Minimization

Bias mitigation is particularly challenging for overparameterized machine learning (ML) models. Overfitting of training points not only amplifies data bias induced by spurious correlations, but also causes the failure of usual bias mitigation methods. To provide actionable insights to address this challenge, we propose a precise analysis of fair empirical risk minimization (ERM) in the overparameterized regime. Importantly, we show that even though conventional fair ERM fails on overparameterized models, this approach can be corrected by modifying the equality fairness constraint to allow for bias overcompensation. Moreover, our analysis presents an empirical criterion for strong equalized odds: balanced group-conditional means of representer coefficients, indicating equal average contribution from each sensitive group. Motivated by this result, we provide an estimable search interval that localizes the required overcompensation level for balanced coefficients. Despite the asymptotic nature of our findings, they closely capture the statistical behavior of moderately large ML models.

SPOT 105 – Mardi 14 avril 2026 15h30 - Exceptionnellement dans l’amphithéâtre Costes de l’ENAC, 7 avenue Edouard Belin, 31400 Toulouse

Sébastien Bourguignon (École Centrale Nantes) – Exact sparse optimization and beyond with branch-and-bound algorithms

Sparse coding in signal processing (also known as variable or subset selection in statistics) aims to approximate a data vector by a linear combination of a small number of elementary features drawn from a high-dimensional dictionary. While the original formulation leads to NP-hard optimization problems based on the $\ell_0$ “norm” (which counts the number of nonzero elements in a vector), most works in the field rely on relaxation techniques or heuristic methods. These approaches can handle very high-dimensional problems, but typically provide sparse solutions without guarantees, and rarely recover the global optimum.
In this talk, we will present different contributions developed in our research group, based on branch-and-bound algorithms that aim to solve exactly the $\ell_0$-norm formulation. Problems involving both standard sparsity and structured sparsity (where groups of variables are jointly constrained to be zero) are considered. Designing tailored continuous relaxations and associated algorithms is shown to play a key role in improving algorithmic efficiency. We show that the proposed algorithms may achieve better data fits than standard approaches on rather small, but difficult, sparse estimation problems, with a much higher, although « reasonable », computation time. A last part will be dedicated to the sparse spectral unmixing problem in signal processing, where sparse estimation is pushed beyond optimization: the branch-and-bound setting is then used to return, with guarantees, the exhaustive set of solutions satisfying acceptable misfit error and sparsity constraints.

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Comité local d’organisation

Une séance par mois environ, avec deux conférenciers chaque fois (deux conférences de type différent : une orientée fondements et une orientée applications, un conférencier de l’environnement toulousain et un conférencier extérieur, un conférencier du milieu académique et un conférencier du milieu de l’industrie et des services, etc.).

Horaire habituel : le lundi après-midi de 14h à 16h.

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Lieu

Sauf indication contraire, à la salle des thèses (C002) à l’ENSEEIHT (N7), 2 rue Charles Camichel, 31000 Toulouse  (métro B, François Verdier). Attention, présentez-vous au poste de garde afin d’accéder au site.

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