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

   Abs arXiv Bib HTML PDF Project

   Motivated by the design of fast reinforcement learning algorithms, see (Croissant et al., 2024), we study the diffusive limit of a class of pure jump ergodic stochastic control problems. We show that, whenever the intensity of jumps \(\varepsilon\,\)is large enough, the approximation error is governed by the Hölder regularity of the Hessian matrix of the solution to the limit ergodic partial differential equation and is, indeed, of order \(\varepsilon^\fracγ2\,\)for all \(γ∈(0,1)\). This extends to this context the results of Abeille et al. (2023) obtained for finite horizon problems. Using the limit as an approximation, instead of directly solving the pre-limit problem, allows for a very significant reduction in the numerical resolution cost of the control problem. Additionally, we explain how error correction terms of this approximation can be constructed under appropriate smoothness assumptions. Finally, we quantify the error induced by the use of the Markov control policy constructed from the numerical finite difference scheme associated to the limit diffusive problem, which seems to be new in the literature and of independent interest.

   @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

   In Proceedings of the 42nd International Conference on Machine Learning 13–19 jul 2025

   Abs Bib HTML PDF 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.

   @inproceedings{Benomar25,
     title = {Pareto-Optimality, Smoothness, and Stochasticity in Learning-Augmented One-Max-Search},
     author = {Benomar, Ziyad and Croissant, Lorenzo and Perchet, Vianney and Angelopoulos, Spyros},
     booktitle = {Proceedings of the 42nd International Conference on Machine Learning},
     pages = {3776--3805},
     year = {2025},
     editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry},
     volume = {267},
     series = {Proceedings of Machine Learning Research},
     month = {13--19 Jul},
     publisher = {PMLR},
   }

3. 

   Bandit Optimal Transport

   Lorenzo Croissant

   Feb 2026

   Abs Bib HTML PDF Project

   Linear bandits have long been a central topic in online learning, with applications ranging from recommendation systems to adaptive clinical trials. Their general learnability has been established when the objective is to minimise the inner product between a cost parameter and the decision variable. While this is highly general, this reliance on an inner product structure belies the name of linear bandits, and fails to account for problems such as Optimal Transport. Using the Kantorovich formulation of Optimal Transport as an example, we show that an inner product structure is not necessary to achieve efficient learning in linear bandits. We propose a refinement of the classical OFUL algorithm that operates by embedding the action set into a Hilbertian subspace, where confidence sets can be built via least-squares estimation. Actions are then constrained to this subspace by penalising optimism. The analysis is completed by leveraging convergence results from penalised (entropic) transport to the Kantorovich problem. Up to this approximation term, the resulting algorithm achieves the same trajectorial regret upper bounds as the OFUL algorithm, which we turn into worst-case regret using functional regression techniques. Its regret interpolates between \(\tilde{O}(\sqrt{T})\,\)and \({O}(T)\), depending on the regularity of the cost function, and recovers the parametric rate \(\tilde{O}(\sqrt{dT})\,\)in finite-dimensional settings.

   @misc{Croissant_BOT_25,
     title = {Bandit {Optimal} {Transport}},
     author = {Croissant, Lorenzo},
     month = feb,
     year = {2026},
     keywords = {Bandit Algorithms, Optimal transport},
   }