Pierre-Cyril Aubin-Frankowski

PhD Student in Machine learning

MINES ParisTech

École des Ponts ParisTech


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.

Contact: pierre-cyril[dot]aubin(at)mines-paristech[dot]fr


  • Kernel Methods
  • Control Theory
  • Optimal Control
  • Nonparametric Estimation
  • Shape constraints


  • PhD in Machine Learning, 2018-2021

    MINES ParisTech

  • MS (M2) in Machine Learning, 2016-2017

    ENS Paris-Saclay

  • MS (M1) in Applied Maths, 2013-2016

    École polytechnique

Recent & Upcoming

-Coming talk at EUROPT 2021, July 2021

-Coming talk at Congrès SMAI 2021, June 2021

-Gave a 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


Anna Korba, PCAF, Szymon Majewski and Pierre Ablin, Kernel Stein Discrepancy Descent, ICML 2021, July 2021, (to appear)

(Under revision) PCAF and Zoltan Szabo, Handling Hard Affine SDP Shape Constraints in RKHSs, January 2021, [article], arXiv, HAL, pdf

PCAF, Linearly-constrained Linear Quadratic Regulator from the viewpoint of kernel methods, SIAM Journal on Control and Optimization, February 2021, (to appear), arXiv, HAL, pdf

PCAF, Interpreting the dual Riccati equation through the LQ reproducing kernel, Comptes Rendus - Mathématique, January 2021, 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, April 2020, article, pdf



PhD student

MINES ParisTech

Sep 2018 – Aug 2021 Paris

Public consultant/Graduate student

AgroParisTech and ENPC

Sep 2017 – Sep 2018 Paris

Hired as top civil servant (Corps des IPEF). Specialized in:

  • Banking and macroeconomics
  • General and Labour law
  • Environmental dialogue

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.


Graduate student

École Normale Supérieure Paris-Saclay

Sep 2016 – Sep 2017 Cachan
Diploma obtained with Highest Honours. Specialized in:

  • General Machine Learning
  • Convex optimization
  • Kernel methods

Graduate student

École polytechnique

Sep 2016 – Sep 2017 Palaiseau
Diploma obtained with Highest Honours. Specialized in:

  • Applied Mathematics
  • Quantum Physics
  • (Neuro)biology