Since September 2018, I am a Ph.D. student at the CAS laboratory at MINES ParisTech (Paris), advised by Nicolas Petit, working on shape/state constraints in optimal control and nonparametric regression through kernel methods. I will defend my PhD in mid-2021, and am interested in the near future in studying connections between kernels and dynamical constrained/controlled systems, among which measures, continuity equations and structured learning problems.
I have recently 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).
My PhD and my lyricomania do not leave me so much time to spare, but I occasionnaly paint.
PhD in Machine Learning, 2018-
MINES ParisTech
MS (M2) in Machine Learning, 2016-2017
ENS Paris-Saclay
MS (M1) in Applied Maths, 2013-2016
École polytechnique
-Coming talk at Learning & Adaptive Systems Group at ETH Zurich (Zurich), February 2021
-Gave a talk at [Séminaire du groupe contrôle] at SIERRA (INRIA Paris), January 2021, slides
-Gave a talk at Séminaire du CAS at MINES ParisTech (Paris), December 2020, slides, video
-Gave a talk at Séminaire de mathématiques appliquées du CERMICS at ENPC (Marne-la-Vallée), October 2020, slides
-Gave a talk at Séminaire DEVI at ENAC (Toulouse), October 2020, slides
-Presented a poster at SPIGL'20, information geometry summer school (Les Houches), July 2020, poster
-Presented a poster at virtual MLSS 2020 Tübingen, machine learning summer school, July 2020, slides
-Gave a talk at virtual IFAC World Congress, July 2020, slides, video
-Gave a talk at virtual European Control Conference, May 2020, slides, video
(Under revision) PCAF and Zoltan Szabo, Handling Hard Affine SDP Shape Constraints in RKHSs, January 2021, [article], arXiv, HAL, pdf
(Under revision) PCAF, Linearly-constrained Linear Quadratic Regulator from the viewpoint of kernel methods, June 2020, [article], arXiv, HAL, pdf
PCAF, Interpreting the dual Riccati equation through the LQ reproducing kernel, Comptes Rendus - Mathématique, December 2020, [article], arXiv, HAL, pdf
PCAF and Zoltan Szabo, Hard Shape-Constrained Kernel Machines, NeurIPS 2020, December 2020, article, arXiv, HAL, pdf
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
PCAF and Jean-Philippe Vert, Gene regulation inference from single-cell RNA-seq data with linear differential equations and velocity inference, Bioinformatics, June 2020, article, biorXiv, pdf, supp
PCAF and Nicolas Petit, Data-driven approximation of differential inclusions and application to detection of transportation modes, Proceedings ECC 2020, May 2020, article, pdf, slides, video
PCAF, Lipschitz regularity of the minimum time function of differential inclusions with state constraints, Systems & Control Letters, May 2020, article, pdf
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.