Centre
Borelli
ENS
Paris-Saclay
PhD candidate in mathematics
I am a PhD student in mathematics at Centre Borelli — École Normale Supérieure Paris-Saclay since 2023, under the supervision of Nicolas Vayatis and Argyris Kalogeratos.
Currently, I am building a framework in where a probabilistic program is written once, then both executed as a sampler and interpreted as a probability measure, so that theorems can be proved about it. I am also interested in the study of global optimization algorithms, especially those modeled as systems of stochastic differential equations. I contribute to and to Mathlib, its community-driven library of formalized mathematics.
You can find details on my academic background in my CV.
For a complete list of my publications, please visit my Google Scholar profile.
McKean-Vlasov (MKV) systems provide a unifying framework for recent state-of-the-art particle-based methods for global optimization. While individual particles follow stochastic trajectories, the probability law evolves deterministically in the mean-field limit, potentially limiting exploration in multimodal landscapes. We introduce two principled approaches to inject noise directly into the probability law dynamics: a perturbative method based on conditional MKV theory, and a geometric approach leveraging tangent space structure. While these approaches are of independent interest, the aim of this work is to apply them to global optimization. Our framework applies generically to any method that can be formulated as a MKV system. Extensive experiments on multimodal objective functions demonstrate that both our noise injection strategies enhance consistently the exploration and convergence across different configurations of dynamics, such as Langevin, Consensus-Based Optimization, and Stein Boltzmann Sampling, providing a versatile toolkit for global optimization.
We introduce an abstract measure‑theoretic framework that serves as a tool to rigorously study stochastic iterative global optimization algorithms as a unified class. The framework is formulated in terms of probability kernels, which, via the Ionescu–Tulcea theorem, induce probability measures on the space of sequences of algorithm iterations, endowed with two intuitive properties. This framework answers the need for a general, implementation‑independent formalism in the analysis of such algorithms, providing a starting point for formalizing global optimization results in proof-assistants. To illustrate the relevance of our tool, we show that common algorithms fit naturally in the framework, and we also use it to give a rigorous proof of a general consistency theorem for stochastic iterative global optimization algorithms (Proposition 3 of [1]). This proof and the entire framework are formalized in the proof assistant. This formalization both ensures the correctness of the definitions and proofs, and provides a basis for future machine-assisted formalizations in the field.
In this paper, we present a deterministic particle-based method for global optimization of continuous Sobolev functions, called Stein Boltzmann Sampling (SBS). SBS initializes uniformly a number of particles representing candidate solutions, then uses the Stein Variational Gradient Descent (SVGD) algorithm to sequentially and deterministically move those particles in order to approximate a target distribution whose mass is concentrated around promising areas of the domain of the optimized function. The target is chosen to be a properly parametrized Boltzmann distribution. For the purpose of global optimization, we adapt the generic SVGD theoretical framework allowing to address more general target distributions over a compact subset of Rd, and we prove SBS’s asymptotic convergence. In addition to the main SBS algorithm, we present two variants: the SBS-PF that includes a particle filtering strategy, and the SBS-HYBRID one that uses SBS or SBS-PF as a continuation after other particle- or distribution-based optimization methods. A detailed comparison with state-of-the-art methods on benchmark functions demonstrates that SBS and its variants are highly competitive, while the combination of the two variants provides the best trade-off between accuracy and computational cost.
In this paper, we propose simple yet effective empirical improvements to the algorithms of the LIPO family, introduced in [1], that we call LIPO+ and AdaLIPO+. We compare our methods to the vanilla versions of the algorithms over standard benchmark functions and show that they converge significantly faster. Finally, we show that the LIPO family is very prone to the curse of dimensionality and tends quickly to Pure Random Search when the dimension increases. We give a proof for this, which is also formalized in the programming language. Source codes and a demo are provided online.
Here is a non-exhaustive list of personal projects I have worked on.
A library that provides tactics to simplify kernel equalities by leveraging categorical reasoning. It automatically translates kernel equalities into equalities in a monoidal category, where powerful tactics from the category theory part of Mathlib can be applied. This project lead to several PRs (#36779; #38211; #38212; #37851) in Mathlib.
GPEP (Generalized Performance Estimation Problems) is a computer-assisted worst-case analyses of first-order optimization methods. It uses symbolic computation to automatically derive worst-case guarantees for any deterministic first-order method on various classes of functions.
Institut des Hautes Études Scientifiques
AISTATS
Collège de France
NeurIPS
IEEE WCCI IJCNN
M.Sc. Mathématique, Vision, Apprentissage
Double B.Sc. Computer Science & Mathematics
Double B.Sc. Mathematics
Double B.Sc. Computer Science & Mathematics
Centre Borelli — École Normale Supérieure Paris-Saclay
Laboratoire Méthodes Formelles
Centre Borelli — École Normale Supérieure Paris-Saclay
Université Paris-Saclay
Université Paris-Saclay
