Research

I study optimization methods for solving large-scale problems arising in signal processing and data science. My research revolves around understanding problems with non-quadratic and non-convex objectives. Among others, I am interested in:

• Mirror descent
• Implicit bias of neural network training
• Nonlinear inverse problems
• Computer-aided performance estimation

I am also interested on the ethical aspects of machine learning and artificial intelligence. I explore topics such as:

• Reliability and robustness of machine learning algorithms
• Political impact of social networks and recommender systems
• Environnmental cost of AI

Teaching

• Optimization for Machine Learning (Télécom Paris, M1)
• Signal processing tools for audio and image (Télécom Paris, L3)
• Numerical analysis (Télécom Paris, L3)
• Ecological and social transition (Télécom Paris, L3)

Preprints

• R-A. Dragomir, Y. Nesterov. Convex Quartic Problems: Homogenized Gradient Method and Preconditioning. [arxiv] [slides] [slides]

Publications

• S. Pesme, R-A. Dragomir, N. Flammarion. Implicit Bias of Mirror Flow on Separable Data.
  NeurIPS, 2024. [arxiv]
• R-A. Dragomir, M. Even, H. Hendrikx. Fast Stochastic Bregman Gradient Methods: Sharp Analysis and Variance Reduction.
  International Conference on Machine Learning, 2021. [PMLR] [arxiv] [slides]
• R-A. Dragomir, A. B. Taylor, A. d'Aspremont, J. Bolte. Optimal Complexity and Certification of Bregman First-Order Methods.
  Mathematical Programming, 2021. [springer] [arxiv] [GeoGebra demo] [code]
• R-A. Dragomir, A. d'Aspremont, J. Bolte. Quartic First-Order Methods for Low-Rank Minimization.
  Journal of Optimization Theory and Applications, 2021. [springer] [arxiv] [code]

Thesis

• R-A. Dragomir, Bregman Gradient Methods for Relatively-Smooth Optimization.
  PhD thesis, 2021. Advised by Jérôme Bolte and Alexandre d'Aspremont. [pdf] [slides] [video]