I am a PhD student in mathematics at Centre Borelli — École Normale Paris-Saclay since 2023, under the supervision of Nicolas Vayatis and Argyris Kalogeratos.

I study and design global optimization algorithms, especially those modeled as systems of stochastic differential equations. I am also particularly interested the formalization of mathematical results using the L∃∀N proof assistant, especially those related to probability theory and optimization algorithms. I contribute to Mathlib, the L∃∀N community-driven library of formalized mathematics.

You can find details on my academic background in my CV.

• Email: gaetan.serre [at] ens-paris-saclay [dot] fr
• Github: @gaetanserre
• Address: Office 3S28, École Normale Supérieure Paris-Saclay

For a complete list of my publications, please visit my Google Scholar profile.

• Enhancing Exploration in Global Optimization by Noise Injection in the Probability Measures Space

  Gaëtan Serré, Pierre Germain, Samuel Gruffaz & Argyris Kalogeratos

  abstract arXiv

  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.

• A Unifying Framework for Global Optimization: From Theory to Formalization

  Gaëtan Serré, Argyris Kalogeratos & Nicolas Vayatis

  abstract arXiv

  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 L∃∀N 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.

• Stein Boltzmann Sampling: A Variational Approach for Global Optimization

  Gaëtan Serré, Argyris Kalogeratos & Nicolas Vayatis

  abstract AISTATS

  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.

• LIPO+: Frugal Global Optimization for Lipschitz Functions

  Gaëtan Serré, Perceval Beja-Battais, Sophia Chirrane, Argyris Kalogeratos & Nicolas Vayatis

  abstract SETN

  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 L∃∀N mathematical language. Source codes and a demo are provided online.

Here is a non-exhaustive list of personal projects I have worked on.

GOB GOB (Global Optimization Benchmark) is a Python package I developed to benchmark global optimization algorithms over a wide range of test functions. It includes C++ implementations of many algorithms as well as various benchmark functions. Github Doc

LipoCons LipoCons is the L∃∀N formalization of the abstract definition of global optimization algorithms presented in [1]. It also includes the formalization of the equivalence between consistency and sampling the whole search space, a proposition introduced in [2]. Github Doc

Kernel-Hom A L∃∀N 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 is useful as it allows to leverage the rich theory of monoidal categories in Mathlib to solve equalities between kernels, which is a common task in the formalization of optimization algorithms and their results. This project lead to a PR (#36779) in Mathlib. Github Doc

GPEP 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. It is based on the PEPit approach: GPEP uses a global optimization solver to relax PEPit's linearity constraints (which, theoretically, allows any algorithm to be symbolically represented in GPEP), at the expense of guarantees and speed. Github

• Stein Boltzmann Sampling

  AISTATS — 2025

• Budding Maths (slides)

  Institut des Hautes Études Scientifiques — 2026

• 1^st prize challenge Accenta

  Collège de France — 2024

• AUTOML Decathlon

  NEURIPS — 2022

• L2RPN competition

  IEEE WCCI IJCNN — 2022

• Introduction to Statistical Learning

  M.Sc. Mathématique, Vision, Apprentissage

• Analyse & Convergence

  Double B.Sc. Computer Science & Mathematics

• Préparation oraux X (Math380X)

  Double B.Sc. Mathematics

• Inférence Statistique

  Double B.Sc. Computer Science & Mathematics

• Pre-PhD on stochastic global optimization and sampling methods

  Centre Borelli — École Normale Supérieure Paris-Saclay, 2023

• Deductive program checking using Why3

  Laboratoire Méthodes Formelles, 2021

• M.Sc. Mathématiques, Vision, Apprentissage

  Centre Borelli — École Normale Supérieure Paris-Saclay, 2022–2023

• M.Sc. Artificial Intelligence

  Université Paris-Saclay, 2021–2022

• Double B.Sc. Mathematics & Computer Science

  Université Paris-Saclay, 2018–2021

Website — I would like to thank Chloé Antoine as this site's design is largely inspired by hers.

Handy tools — Typst: a modern LaTeX alternative; Lazygit: a simple terminal UI for git

Play & learn — L∃∀N Game Server: games to learn about L∃∀N and its mathematical library; Learn Git Branching: an interactive way to learn git

Non-academic interests — I enjoy travel photography (you can find some on this site), cataloguing and commenting on films, TV shows and video games on SensCritique, collecting audio equipment (currently on repeat: Dire Straits, Telegraph Road), and cheering for my favorite LoL esports team.