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.

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.

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.