Pierre-Cyril Aubin-Frankowski

Post-doctoral researcher in Machine learning



  • If you want an overview of some of my research up to July 2023 concerning optimization and kernels, here are some slides

  • New article with Alain Bensoussan, on the RKHSs of push-forward maps for mean-field control,

  • New article with Flavien Léger, on alternating minimization and gradient descent with a general cost, slides

  • New article in Pure and Applied Functional Analysis, with Alain Bensoussan, on the RKHSs of Kalman filtering,


Moving to the dark side of the optimization world! I joined as postdoc the VADOR team at TU Wien with Aris Daniilidis for 23/24.

From September 2021 to August 2023, I was a post-doctoral researcher at INRIA SIERRA, working with Alessandro Rudi. I obtained my PhD in July 2021 from PSL MINES ParisTech (Paris), at the CAS laboratory, working on shape/state constraints in optimal control and nonparametric regression through kernel methods (manuscript, slides). 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).

I am interested in the links between kernel methods, optimal control, Kalman filtering and optimization in measure spaces. So far I have shown that kernels appear in linear-quadratic optimal control because of Hilbertian vector spaces of trajectories, while, for estimation problems, they appear through covariances of Gaussian processes. It is this dual, deterministic and stochastic, nature of kernels which underlies the duality between optimal control and estimation in the Linear-Quadratic case. Kernels even extend to mean-field control article

My latest focus is on optimization problems where the distance is replaced by a generic cost function (article). The natural algorithm here is alternating minimization for which we gave novel rates with Flavien Léger. I also study sign-reversing involutions on max-plus spaces with Stéphane Gaubert.

My research and my lyricomania, a passion I share within the association Juvenilia, do not leave me so much time to spare, but I occasionnaly paint.

Contact: pierre-cyril[dot]aubin(at)tuwien[dot]ac[dot]at


  • Kernel Methods
  • Optimal Control
  • Optimization with general costs
  • Abstract convexity


  • Postdoc in Optimization, 2023-

    TU Wien

  • Postdoc in Machine Learning, 2021-2023

    INRIA Paris

  • PhD in Machine Learning & Control Theory, 2018-2021

    MINES ParisTech

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

    ENS Paris-Saclay

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

    École polytechnique


  1. (submitted) PCAF, Alain Bensoussan, Reproducing kernel approach to linear quadratic mean field control problems, August 2023, arXiv

  2. (to appear) PCAF, Alain Bensoussan, S. Joe Qin, Alternating minimization for simultaneous estimation of a latent variable and identification of a linear continuous-time dynamic system, August 2023, Communications in Optimization Theory, arXiv

  3. (submitted) Flavien Léger, PCAF, Gradient descent with a general cost, May 2023, arXiv, slides

  4. (submitted) PCAF, Alessandro Rudi, Approximation of optimization problems with constraints through kernel Sum-Of-Squares, January 2023, arXiv, slides

  5. (to appear) PCAF, Stéphane Gaubert, Tropical reproducing kernels and optimization, Integral Equations and Operator Theory, December 2022, arXiv, slides

  6. PCAF and Zoltán Szabó, Handling Hard Affine SDP Shape Constraints in RKHSs, November 2022, JMLR, article, arXiv, HAL, code

  7. (to appear) PCAF, Alain Bensoussan, The reproducing kernel Hilbert spaces underlying linear SDE Estimation, Kalman filtering and their relation to optimal control, August 2022, Pure and Applied Functional Analysis, arXiv, slides

  8. PCAF, Anna Korba, Flavien Léger, Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and EM, December 2022, NeurIPS 2022, arXiv, slides (short), slides (long), poster

  9. PCAF, Alain Bensoussan, Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems, June 2022, CDC 2022, article, arXiv, slides

  10. PCAF, Stability of solutions for controlled nonlinear systems under perturbation of state constraints, June 2022, IFAC CAO 2022, article, arXiv, slides

  11. Anna Korba, PCAF, Szymon Majewski and Pierre Ablin, Kernel Stein Discrepancy Descent, ICML 2021 (long oral), July 2021, article, arXiv, code/website, pdf, slides, poster

  12. PCAF, Linearly-constrained Linear Quadratic Regulator from the viewpoint of kernel methods, SIAM Journal on Control and Optimization, February 2021, article, arXiv, HAL, pdf, code, slides

  13. PCAF, Interpreting the dual Riccati equation through the LQ reproducing kernel, Comptes Rendus - Mathématique, January 2021, article, arXiv, HAL, pdf, slides

  14. PCAF and Zoltán Szabó, Hard Shape-Constrained Kernel Machines, NeurIPS 2020, December 2020, article, arXiv, HAL, pdf, code

  15. PCAF, Nicolas Petit and Zoltán Szabó, Kernel Regression for Trajectory Reconstruction of Vehicles under Speed and Inter-Vehicular Distance Constraints, Proceedings IFAC WC 2020, July 2020, article, pdf, slides, video

  16. 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, code

  17. 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

  18. PCAF, Lipschitz regularity of the minimum time function of differential inclusions with state constraints, Systems & Control Letters, April 2020, article, pdf

Recent & Upcoming


Jan 2023 – Present

Jan 2022 – Dec 2022
  • Talk in invited session at CDC22 on LQ kernel for PDE control, December
  • Talk in invited session at NeurIPS22 on mirror descent in measure spaces, December
  • Talk in invited session at MTNS22 on stability of trajectories under constraint perturbation, September
  • Talk in invited session at ORCOS-VC22 on LQ kernel for state constraints, July
  • Talk in invited session at IFAC-CAO on stability of trajectories under constraint perturbation, July
  • Talk in invited session at EURO22 on handling with kernels infinitely many constraints through a finite number, July
  • Talk in invited session at FGP2022, May
  • Talk at Séminaire Parisien d'Optimisation, February
  • Talk at GdT Contrôle on LQ kernel for state constraints, January
  • Award of best post-doc presentation at Lifting Inference with Kernel Embeddings LIKE22 Bern, January

Jan 2021 – Dec 2021

Jan 2020 – Dec 2020