New article with Yohann de Castro, Axel Parmentier, Alessandro Rudi, on Surrogate Policies for Combinatorial Optimization Problems, slides
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
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 (see arXiv, slides with Alain Bensoussan). Kernels even extend to mean-field control (article).
My latest focus is on optimization problems where the notion of 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 work on 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.
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
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
(to appear) PCAF, Alain Bensoussan, Reproducing Kernel Approach to Linear-Quadratic Mean Field Control Problems with Additive Noise, July 2024, CDC 2024
(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
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