Pierre-Cyril Aubin-Frankowski

Post-doctoral researcher in Optimization and Machine learning

TU Wien, VADOR

News

New article with Stéphane Gaubert, on the characterization of order isomorphisms, 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
If you want an overview of some of my research up to July 2023 concerning optimization and kernels, here are some slides

Biography

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 workon the characterization of order isomorphisms with Stéphane Gaubert (article and slides).

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

Interests

Kernel Methods
Optimal Control
Optimization with general costs
Abstract convexity

Education

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

Publications

(submitted) PCAF, Stéphane Gaubert, Order isomorphisms of sup-stable function spaces: continuous, Lipschitz, c-convex, and beyond, April 2024, arXiv, slides
(submitted) PCAF, Alain Bensoussan, Reproducing kernel approach to linear quadratic mean field control problems, August 2023, arXiv
(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
(submitted) Flavien Léger, PCAF, Gradient descent with a general cost, May 2023, arXiv, slides
PCAF, Alessandro Rudi, Approximation of optimization problems with constraints through kernel Sum-Of-Squares, Optimization, February 2024, article, arXiv, slides
(to appear) PCAF, Stéphane Gaubert, Tropical reproducing kernels and optimization, Integral Equations and Operator Theory, December 2022, arXiv, slides
PCAF and Zoltán Szabó, Handling Hard Affine SDP Shape Constraints in RKHSs, November 2022, JMLR, article, arXiv, HAL, code
(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
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
PCAF, Alain Bensoussan, Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems, June 2022, CDC 2022, article, arXiv, slides
PCAF, Stability of solutions for controlled nonlinear systems under perturbation of state constraints, June 2022, IFAC CAO 2022, article, arXiv, slides
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
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
PCAF, Interpreting the dual Riccati equation through the LQ reproducing kernel, Comptes Rendus - Mathématique, January 2021, article, arXiv, HAL, pdf, slides
PCAF and Zoltán Szabó, Hard Shape-Constrained Kernel Machines, NeurIPS 2020, December 2020, article, arXiv, HAL, pdf, code
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
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
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

Recent & Upcoming

Jan 2024 – Present

Gave a talk at TU Wien, VADOR on the characterization of order isomorphisms, April
Gave a talk at SMAI MODE, Lyon on extending gradient descent and convexity, March. I won the Prix Dodu for the best communication!

Jan 2023 – Dec 2023

Gave an online talk at Alan Turing Institute, Machine Learning and Dynamical Systems Seminar, full video available, December
Gave a talk at 3rd Austrian Calculus of Variations Day hosted at TU Wien, on extending gradient descent and convexity, November
Gave a talk at Uni Wien, optimization seminar on extending gradient descent and convexity, October
Gave a talk at TU Wien, VADOR on gradient descent with general cost, September
Gave a talk at Google DeepMind on alternating minimization and tropical kernels, August
Gave a talk at LIKE23 organized at Uni Bern on going beyond Hilbertian kernels, June
Poster at workshop on Computational OT organized within FoCM 2023 in Paris, June
Poster at workshop on emerging topics in OT organized at ETH Zurich Institute for Theoretical Studies, June
Gave a seminar at MaLGa organized at Uni Genova on gradient descent with general cost, May
Participation to workshop on OT, mean-field and ML organized at IAS TU Munich, April
Talk at GdT-OT of IM Orsay on tropical kernels and optimization, February

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

Talk at PGMO DAYS 2021, December
Talk at CEMRACS 2021 on model order reduction by spectral gap optimization, August
Research project at CEMRACS 2021 on estimating reaction coordinates and the Poincaré constant in a metasbility context, July-August
Talk at CEMRACS 2021 on sampling distributions through gradient flows via the kernel Stein discrepancy descent, July
Talk at CT 2021 on LQ kernel for state constraints video, July
talk at Congrès SMAI 2021 slides, June
Talk at Learning & Adaptive Systems Group at ETH Zurich (Zurich), February
Talk at Séminaire du groupe contrôle at SIERRA (INRIA Paris)slides, January

Jan 2020 – Dec 2020

Talk at Séminaire du CAS at MINES ParisTech (Paris) on the LQ kernel slides, video, December
Talk at Séminaire de mathématiques appliquées du CERMICS at ENPC (Marne-la-Vallée) on shape/state constraints through kernels slides, October
Talk at Séminaire DEVI at ENAC (Toulouse) slides, October
Poster at SPIGL'20, information geometry summer school (Les Houches), poster on shape constraints handled through SOC and kernels, July
Poster at virtual MLSS 2020 Tübingen, machine learning summer school, slides, July
Talk at virtual IFAC World Congress, slides on reconstructing trajectories with side information, kernel methods and SOC cosntraints, video, July
Talk at virtual European Control Conference 2020, slides on identifying mode of transportation by delimiting areas through SVDD, video, May