Pierre-Cyril Aubin-Frankowski
Researcher/Associate professor in Optimization and Machine learning
CERMICS, ENPC, IPP
News
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New arXiv with Gabriele Todeschi and Virginie Ehrlacher on Debiasing optimal transport: classical and entropic, with novel inf-representations for EOT. Stay tuned for quantum OT!
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New arXiv with Giacomo Enrico Sodini and Ulisse Stefanelli on Evolution variational inequalities with general costs, (slides) (accepted at Journal of Functional Analysis, March 2026, article)
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New arXiv with Yohann de Castro, Axel Parmentier, Alessandro Rudi, on Surrogate Policies for Combinatorial Optimization Problems, (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). Both directions unite in article on novel inf-representations for entropic optimal transport.
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).
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If you want an overview of some of my research up to July 2023 concerning optimization and kernels, here are some (slides).
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If you want an overview of some of my research up to November 2025 concerning gradient flows with general costs, here is a video.
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.
Interests
- Optimization with general costs
- Flows on measure spaces
- Kernel Methods
- Optimal Control
Education
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Postdoc in Optimization, 2023-2024
TU Wien
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Postdoc in Machine Learning, 2021-2023
INRIA Paris
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PhD in Machine Learning & Control Theory, 2018-2021
MINES ParisTech
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MS (M2) in Machine Learning, 2016-2017
ENS Paris-Saclay
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MS (M1) in Applied Maths, 2013-2016
École polytechnique