Marc-H Lambert

Engineer at DGA and Researcher at Sierra [https://www.di.ens.fr/sierra/] INRIA-ENS Rue Simone-Iff, Paris marc.lambert [@] inria [DOT] fr Google scholar: [https://scholar.google.com/citations?user=a2HnQ6oAAAAJ&hl=fr]

About me

After a MSc in machine learning (MVA), I obtained a PhD in November 2024 under the supervision of Francis Bach and Silvère Bonnabel. My main research focus on the interface between machine learning and robotics using variational inference to build new algorithms for online learning, kalman filtering and stochastic control. I also work part-time as a research engineer on smart sensors (infrared camera and radar) at the French Defense Procurement Agency.

Research

I work on new algorithms for inference, filtering and control based on the variational approximation of a target distribution with a Gaussian or a mixture of Gaussians.

More specifically, we have developed the concept of Gaussian particles as elements of the Wasserstein space of measures taking values on the Bures–Gaussian manifold. We also apply variational inference for dynamic systems through the introduction of variational dynamic programming.

My research interests include:

• Variational inference

• Optimal transport

• Stochatic control

• Bayesian Machine Learning

• Kalman filtering

• Robotics

PHD Thesis

Variational Methods for Inference, Filtering, and Control. [https://inria.hal.science/tel-05016387]

Publications

• The LQR-Schrödinger Bridge. ML. 2025. CDC. [https://inria.hal.science/view/index/docid/5108441]

• Variational Inference with Mixtures of Isotropic Gaussians. M. Petit Talamon, ML, A. Korba. 2025. [http://arxiv.org/abs/2506.13613]

• Entropy Regularized Variational Dynamic Programming for Stochastic Optimal Control. ML, F. Bach, S. Bonnabel. 2025. [https://theses.hal.science/INRIA/hal-05016406v1]

• Variational Dynamic Programming for Stochastic Optimal Control. ML, S. Bonnabel and F. Bach
  2024. CDC. [https://arxiv.org/abs/2404.14806]

• Low-rank plus diagonal approximations for Riccati-like matrix differential equations. S. Bonnabel, ML and F. Bach
  2024 Journal on Matrix Analysis and Applications (SIMAX). [https://inria.hal.science/hal-04621158v1/document]

• Variational Gaussian Approximation of the Kushner Optimal Filter. ML, S. Bonnabel and F. Bach
  2023 International Conference on Geometric Science of Information, 395-404 [https://arxiv.org/pdf/2310.01859.pdf]

• Variational inference via Wasserstein gradient flows. ML, S. Chewi, F. Bach, S. Bonnabel and P Rigollet
  2022 Advances in Neural Information Processing Systems [https://arxiv.org/abs/2205.15902]

• The continuous-discrete variational Kalman filter (CD-VKF). ML, S. Bonnabel and F. Bach
  2022 IEEE 61st Conference on Decision and Control (CDC), 6632-6639 [https://inria.hal.science/hal-03665666v2/document]

• The limited-memory recursive variational Gaussian approximation (L-RVGA). ML, S. Bonnabel and F. Bach
  2023 Statistics and Computing 33 (3), 70 [https://arxiv.org/pdf/2303.14195.pdf]

• The recursive variational Gaussian approximation (R-VGA). ML, S. Bonnabel and F. Bach
  2021 Statistics and Computing 32 (1), 10 [https://inria.hal.science/hal-03086627/file/RVGA-HAL-v2.pdf]

Reviewer for:

• Annual Conference on Neural Information Processing Systems (NeurIPS)

• Journal of Transactions on Automatic Control (TAC)

• Journal of Transactions on Signal Processing (TSP)

• Conference on Decision and Control (CDC)

Code

The algorithms associated to these articles are available here: [https://github.com/marc-h-lambert]