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 in measure theory and in the formalization of optimization algorithms and their results using the L∃∀N proof assistant. I contribute to Mathlib, its mathematics library.

• 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.

• Formal equivalence between global optimization consistency and random search

  Gaëtan Serré

  abstract arXiv

  We formalize a proof that any stochastic and iterative global optimization algorithm is consistent over Lipschitz continuous functions if and only if it samples the whole search space. To achieve this, we use the L∃∀N theorem prover and the Mathlib library. The major challenge of this formalization, apart from the technical aspects of the proof itself, is to converge to a definition of a stochastic and iterative global optimization algorithm that is both general enough to encompass all algorithms of this type and specific enough to be used in a formal proof. We define such an algorithm as a pair of an initial probability measure and a sequence of Markov kernels that describe the distribution of the next point sampled by the algorithm given the previous points and their evaluations. We then construct a probability measure on finite and infinite sequences of iterations of the algorithm using the Ionescu-Tulcea theorem.

• 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

• Stein Boltzmann Sampling

  AISTATS — 2025

• 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

• 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: L'Impératrice, Me Da Igual), and cheering for my favorite LoL esports team.