arXiv subjects

Gaëtan Serré

Publications and source records attributed to Gaëtan Serré.

6 recordsLinked to original sources

arXiv2026

A Unifying Framework for Global Optimization: From Theory to Formalization

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 (Malherbe, et al., 2017). This proof and the entire framework are formalized in the Lean 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.

cs.FL↗

arXiv2026

GLOBe: A Modular Global Optimization library

Open-source libraries are have a catalytic role in research pipelines, where new methods must be compared against up-to-date baselines. We present the GLobal Optimization Benchmark (GLOBe) modular Python library that unifies classical and recent continuous global optimization algorithms, including decision-based and mathematically founded particle-based methods, in a single framework. A central contribution of GLOBe is its modular architecture, which factors common algorithmic patterns into reusable familyl evel components and enables plugins to be implemented once and makes them available to all algorithms in the corresponding family. This modular design leverages recent advances in mathematical formalization of global optimization, where structural commonalities across algorithms have been identified and used to develop broadly applicable, formally grounded algorithmic features. The C++ backend relies on Eigen 5 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.

math.OC↗

arXiv2026

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

McKean-Vlasov (MKV) systems provide a unifying framework for recent state-of-the-art particlebased 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.

math.OC↗

arXiv2025

Stein Boltzmann Sampling: A Variational Approach for Global Optimization

In this paper, we present a flow-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 $\mathbb{R}^d$, 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.

math.OC↗

arXiv2024

LIPO+: Frugal Global Optimization for Lipschitz Functions

In this paper, we propose simple yet effective empirical improvements to the algorithms of the LIPO family, introduced in [Malherbe2017], 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 Lean mathematical language. Source codes and a demo are provided online.

math.OC↗

arXiv2022

Reinforcement learning for Energies of the future and carbon neutrality: a Challenge Design

Current rapid changes in climate increase the urgency to change energy production and consumption management, to reduce carbon and other green-house gas production. In this context, the French electricity network management company RTE (R{é}seau de Transport d'{É}lectricit{é}) has recently published the results of an extensive study outlining various scenarios for tomorrow's French power management. We propose a challenge that will test the viability of such a scenario. The goal is to control electricity transportation in power networks, while pursuing multiple objectives: balancing production and consumption, minimizing energetic losses, and keeping people and equipment safe and particularly avoiding catastrophic failures. While the importance of the application provides a goal in itself, this challenge also aims to push the state-of-the-art in a branch of Artificial Intelligence (AI) called Reinforcement Learning (RL), which offers new possibilities to tackle control problems. In particular, various aspects of the combination of Deep Learning and RL called Deep Reinforcement Learning remain to be harnessed in this application domain. This challenge belongs to a series started in 2019 under the name "Learning to run a power network" (L2RPN). In this new edition, we introduce new more realistic scenarios proposed by RTE to reach carbon neutrality by 2050, retiring fossil fuel electricity production, increasing proportions of renewable and nuclear energy and introducing batteries. Furthermore, we provide a baseline using state-of-the-art reinforcement learning algorithm to stimulate the future participants.

cs.AI↗