I obtained my PhD in July 2021 from PSL MINES ParisTech (Paris), at the CAS laboratory, where I was advised by Nicolas Petit, working on shape/state constraints in optimal control and nonparametric regression through kernel methods. This revolves around optimization problems in infinite dimensions with infinitely many constraints. I am interested in the near future in studying connections between kernels and dynamical constrained/controlled systems, among which measures, continuity equations (see ICML21) and structured learning problems.
During my PhD, I defined a new positive definite kernel, dubbed the Linear-Quadratic kernel. It is a matrix-valued reproducing kernel, instrumental in Linear-Quadratic optimal control, related to the Gramian of controllability and to the dual Riccati equation (see pdf for an introduction and pdf for the application to state constraints).
I have also developped a general, convex and modular framework to handle shape constraints in RKHSs (see pdf), applied for instance to trajectory reconstruction (see NeuriPS 2020 video for a quick overview in 180s). This is a line of work, originally inspired by non-crossing quantile regression, with Zoltán Szabó. We were particularly motivated by econometrics and finance studies.
I graduated from École polytechnique (X2013) in 2017, then obtained my Master degree (MVA, Mathematics-Vision-Learning) with Highest Honours after an internship with Jean-Philippe Vert (CBIO-Google) on gene network inference (based on single-cell RNA sequencing).
PhD in Machine Learning, 2018-2021
MS (M2) in Machine Learning, 2016-2017
MS (M1) in Applied Maths, 2013-2016
-I attended CEMRACS 2021, July-August 2021
PCAF, Nicolas Petit and Zoltan Szabo, Kernel Regression for Trajectory Reconstruction of Vehicles under Speed and Inter-Vehicular Distance Constraints, Proceedings IFAC WC 2020, July 2020, article, pdf, slides, video
Title: Estimation and Control under Constraints through Kernel Methods.
Abstract: Pointwise state and shape constraints in control theory and nonparametric estimation are difficult to handle as they often involve convex optimization problem with an infinite number of inequality constraints. Satisfaction of these constraints is critical in many applications, such as path-planning or joint quantile regression. Reproducing kernels are propitious for pointwise evaluations. However representer theorems, which ensure the numerical applicability of kernels, cannot be applied for an infinite number of evaluations. Through constructive algebraic and geometric arguments, we prove that an infinite number of affine real-valued constraints over derivatives of the model can be tightened into a finite number of second-order cone constraints when looking for functions in vector-valued reproducing kernel Hilbert spaces. We show that state-constrained Linear-Quadratic (LQ) optimal control is a shape-constrained regression over the Hilbert space of linearly-controlled trajectories defined by an explicit LQ kernel related to the Riccati matrix. The efficiency of the developed approach is illustrated on various examples from both linear control theory and nonparametric estimation. Finally, we provide some results for general differential inclusions in minimal time problems and identification of the graph of the set-valued map. Most of all we bring to light a novel connection between reproducing kernels and optimal control theory, identifying the Hilbertian kernel of linearly controlled trajectories.
Hired as top civil servant (Corps des IPEF). Specialized in:
Worked on artificial intelligence tailored to the strategies of the technical and scientific network of the French Ministry of Environment. I handed a report shortly after the Villani mission “For a meaningful Artificial Intelligence”. This report focuses on conceptualizing machine learning approaches and details its possible effects in institutions transforming due to the Digital Revolution.