About

Publications

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

1. SETN2026

   GLOBe: A Modular Global Optimization Library

   Gaëtan Serré, Argyris Kalogeratos & Nicolas Vayatis

   Abstract SETN

   Open-source libraries play a catalytic role in research pipelines, where new methods must be compared against up-to-date baselines. We present the GLobal Optimization Benchmark (GLOBe), a modular Python library for continuous global optimization, often in a black-box setting, that unifies classical and recent algorithms, including decision-based and particle-based methods, in a single framework. Its central contribution is a modular architecture that factors common algorithmic patterns into reusable family-level components, so that plugins are implemented once and made available to all algorithms of the corresponding family. This design leverages recent advances in the mathematical formalization of global optimization, where structural commonalities across algorithms have been identified and used to develop broadly applicable, formally grounded features. With a C++ backend relying on Eigen for efficient linear algebra, GLOBe presently includes 14 optimizers, 19 analytical benchmarks along with a random function generator, and an integrated toolkit for direct algorithm comparison.

2. arXiv2026

   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.

3. arXiv2025

   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 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.

4. AISTATS2025

   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 R^d, 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.

5. SETN2024

   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 the programming language. Source codes and a demo are provided online.

& Mathlib

I contribute to Mathlib, the library of formalized mathematics of , mostly in probability and measure theory, and occasionally to itself. Here are my main contributions; see also the full lists of my merged pull requests to Mathlib and to .

Markov categories

The category of measurable spaces and s-finite kernels, a copy-discard category, and its subcategory of Markov kernels, a positive Markov category. Deterministic kernels. #36779 #37851 #38211 #38212

Floating point

In itself: the fused multiply-add of floating-point numbers, Float.fma and Float32.fma, with a logical model. lean4#15024

Randomness of kernels

Any Markov kernel with values in a standard Borel space is the image of the uniform measure on [0, 1] under a measurable map (Kallenberg, Foundations of Modern Probability, Lemma 4.22). Along the way: the sigmoid function, measurable embeddings of standard Borel spaces into [0, 1], and the Lebesgue measure of its intervals. #30112 #28780 #27517 #27513

Gaussian distributions

Real and multivariate Gaussian distributions are measurable functions of their parameters. Along the way: a measurable structure on matrices, the measurability of the matrix square root, and the isometric continuous functional calculus of matrices. #40117 #42948 #42621 #40272

Measure theory

Measures with density and conditional expectations under weaker assumptions, the law of total probability, and Lebesgue integrals with respect to the trajectories of the Ionescu-Tulcea theorem. #13340 #13314 #13932 #28731

Projects

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

1. 

   · Mathlib

   Kernel-Hom

   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 in Mathlib (#36779; #38211; #38212; #37851).

   GitHubDoc

2. 

   Python · C++

   GLOBe

   GLOBe (Global Optimization Benchmark) is a Python package 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.

   GitHubDoc

3. 

   · Formalization

   LipoCons

   LipoCons is the 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].

   GitHubDoc

4. 

   Worst-case analysis

   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.

   GitHub

Talks

1. 2026

   Institut des Hautes Études Scientifiques

   Budding Maths slides

2. 2025

   AISTATS

   Stein Boltzmann Sampling

3. 2024

   Collège de France

   1^st prize challenge Accenta

4. 2022

   NeurIPS

   AutoML Decathlon

5. 2022

   IEEE WCCI IJCNN

   L2RPN competition

Teaching

• 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

Miscellaneous

Website

This website is inspired by the site of NYC Lean. The cross-stitched name and its blue thread are a nod to the poster of the exhibition Extraordinary — 시간이 쌓이는 순간 (Seoul Museum, 2026), and the buttons and the needle to Henry Selick's Coraline (2009), from which the other colors are sampled. The previous design was largely inspired by Chloé Antoine's.

Handy tools

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

Play & learn

Game Server: games to learn about 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), cataloging 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.