Pierre-Cyril Aubin-Frankowski

Researcher/Associate professor in Optimization and Machine learning

CERMICS, ENPC, IPP

News

New article with Giacomo Enrico Sodini and Ulisse Stefanelli on Evolution variational inequalities with general costs, (slides)
New article with Yohann de Castro, Axel Parmentier, Alessandro Rudi, on Surrogate Policies for Combinatorial Optimization Problems, (slides)
If you want an overview of some of my research up to July 2023 concerning optimization and kernels, here are some (slides).

Biography

I am an associate professor at Ecole des Ponts ParisTech and a researcher at CERMICS, in the Optimization team. I am interested in the relations between optimization algorithms in finite and infinite dimensions, their convergence properties and the associated notions of convexity. My main playfield is optimization in the space of probability measures, in connection with optimal transport theory and optimal control. We develop applications of these methods with Axel Parmentier for operations research, working in particular with Air France.

My latest focus is on optimization problems where the notion of distance is replaced by a generic cost function (slides), e.g., Bregman divergences. The natural algorithm here is alternating minimization (article) and the convergence assumptions and limit flow are related to Evolution Variational Inequalities (article). I also work on the characterization of order isomorphisms with Stéphane Gaubert (article and slides).

I was a post-doctoral researcher in 2023-24 at TU Wien VADOR with Aris Daniilidis; in 2021-23 at INRIA SIERRA, with Alessandro Rudi. I obtained my PhD in July 2021 from École des Mines Paris – PSL (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 on gene network inference (based on single-cell RNA sequencing).

Follow-ups on my PhD tackle 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 (see arXiv, slides with Alain Bensoussan). Kernels even extend to mean-field control (article).

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)enpc[dot]fr

Interests

Optimization with general costs
Flows on measure spaces
Kernel Methods
Optimal Control

Education

Postdoc in Optimization, 2023-2024

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, Giacomo Enrico Sodini, Ulisse Stefanelli, Evolution variational inequalities with general costs, May 2025, arXiv, slides
Clément Bonet, Théo Uscidda, Adam David, PCAF, Anna Korba, Mirror and Preconditioned Gradient Descent in Wasserstein Space, June 2024, NeurIPS 2024 (spotlight), arXiv, slides (long)
(submitted) PCAF, Yohann de Castro, Axel Parmentier, Alessandro Rudi, Generalization Bounds of Surrogate Policies for Combinatorial Optimization Problems, July 2024, arXiv, slides
PCAF, Alain Bensoussan, Reproducing Kernel Approach to Linear-Quadratic Mean Field Control Problems with Additive Noise, July 2024, article, CDC 2024
PCAF, Stéphane Gaubert, Order isomorphisms of sup-stable function spaces: continuous, Lipschitz, c-convex, and beyond, April 2024, Communications in Contemporary Mathematics, arXiv, slides
(submitted) PCAF, Alain Bensoussan, Reproducing kernel approach to linear quadratic mean field control problems, August 2023, arXiv
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, article
(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
PCAF, Stéphane Gaubert, Tropical reproducing kernels and optimization, Integral Equations and Operator Theory, December 2022, article, arXiv, slides
PCAF and Zoltán Szabó, Handling Hard Affine SDP Shape Constraints in RKHSs, November 2022, JMLR, article, arXiv, HAL, code
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 2025 – Present

Talk on gradient flows with c-cost at Colloquium Bézout UGE, June
Talk on gradient flows with c-cost at Thoth seminar in Grenoble, June
Talk on gradient flows at a Groupe de travail, LPSM, March
Lecturing course on Decision in Uncertainty (Markov chains, Bellman equations) at ENPC Jan-March

Jan 2024 – Dec 2024

New position as associate professor at ENPC
Talk at 4th Austrian Calculus of Variations Day hosted at Uni Innsbruck, on gradient flow beyond metric spaces, November
Talk at MeRiOT, School and Conference on Metric Measure Spaces, Ricci Curvature, and Optimal Transport, September
Talk at One World Optimization Seminar in Vienna on extending gradient descent and convexity, June
Talk at NAO 2024 in Erice on extending gradient descent and convexity, May
Talk at TU Wien, VADOR on the characterization of order isomorphisms, April
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
Talk at 3rd Austrian Calculus of Variations Day hosted at TU Wien, on extending gradient descent and convexity, November
Talk at Uni Wien, optimization seminar on extending gradient descent and convexity, October
Talk at TU Wien, VADOR on gradient descent with general cost, September
Talk at Google DeepMind on alternating minimization and tropical kernels, August
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
Talk 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