Lorenzo Croissant

selected publications

1. 

   Diffusive limit approximation of pure jump optimal ergodic control problems

   Marc Abeille, Bruno Bouchard, and Lorenzo Croissant

   Stochastic Processes and their Applications Mar 2025

   arXiv Bib HTML PDF Blog Project

   @article{ABC25,
     title = {Diffusive limit approximation of pure jump optimal ergodic control problems},
     volume = {181},
     copyright = {All rights reserved},
     issn = {03044149},
     doi = {10.1016/j.spa.2024.104536},
     language = {en},
     urldate = {2024-12-05},
     journal = {Stochastic Processes and their Applications},
     author = {Abeille, Marc and Bouchard, Bruno and Croissant, Lorenzo},
     month = mar,
     year = {2025},
     pages = {104536},
   }

2. 

   Pareto-Optimality, Smoothness, and Stochasticity in Learning-Augmented One-Max-Search

   Ziyad Benomar, Lorenzo Croissant, Vianney Perchet, and 1 more author

   Feb 2025

   Abs arXiv Bib HTML PDF Blog Project

   One-max search is a classic problem in online decision-making, in which a trader acts on a sequence of revealed prices and accepts one of them irrevocably to maximise its profit. The problem has been studied both in probabilistic and in worst-case settings, notably through competitive analysis, and more recently in learning-augmented settings in which the trader has access to a prediction on the sequence. However, existing approaches either lack smoothness, or do not achieve optimal worst-case guarantees: they do not attain the best possible trade-off between the consistency and the robustness of the algorithm. We close this gap by presenting the first algorithm that simultaneously achieves both of these important objectives. Furthermore, we show how to leverage the obtained smoothness to provide an analysis of one-max search in stochastic learning-augmented settings which capture randomness in both the observed prices and the prediction.

   @misc{Benomar25,
     title = {Pareto-{Optimality}, {Smoothness}, and {Stochasticity} in {Learning}-{Augmented} {One}-{Max}-{Search}},
     copyright = {All rights reserved},
     urldate = {2025-02-11},
     publisher = {arXiv},
     author = {Benomar, Ziyad and Croissant, Lorenzo and Perchet, Vianney and Angelopoulos, Spyros},
     month = feb,
     year = {2025},
     keywords = {Computer Science - Artificial Intelligence, Computer Science - Data Structures and Algorithms},
   }

3. 

   Bandit Optimal Transport

   Lorenzo Croissant

   Feb 2025

   Abs arXiv Bib HTML PDF Blog Project

   Despite the impressive progress in statistical Optimal Transport (OT) in recent years, there has been little interest in the study of the }emph{sequential learning} of OT. Surprisingly so, as this problem is both practically motivated and a challenging extension of existing settings such as linear bandits. This article considers (for the first time) the stochastic bandit problem of learning to solve generic Kantorovich and entropic OT problems from repeated interactions when the marginals are known but the cost is unknown. We provide \tildeO(\sqrtT) regret algorithms for both problems by extending linear bandits on Hilbert spaces. These results provide a reduction to infinite-dimensional linear bandits. To deal with the dimension, we provide a method to exploit the intrinsic regularity of the cost to learn, yielding corresponding regret bounds which interpolate between \tildeO(\sqrtT) and \tildeO(T).

   @misc{Croissant_BOT_25,
     title = {Bandit {Optimal} {Transport}},
     author = {Croissant, Lorenzo},
     month = feb,
     year = {2025},
     keywords = {Bandit Algorithms, Optimal transport},
   }