The goal of my thesis is to build a systematic procedure for finding the best performing optimization methods for a given structured problem.This research went into two directions:
First, I worked on applications where I analyzed specific structured problems to identify the best performing optimization methods.
Second, I focused on developing the systematic procedure mentioned earlier.
The projects below are in reverse chronological order.
Under review With Samuel Vaiter and Yassine Laguel, we introduce BADR, a bilevel framework to compute Pareto-efficient models compatible with any fairness metric: a lower level performs weighted risk minimization across groups while an upper level optimizes the chosen fairness objective. We propose two scalable algorithms with convergence guarantees, released as an open-source Python toolbox, and show they outperform existing Pareto-efficient fairness approaches.
Ongoing work With François Glineur, we propose a modeling language that aims at describing oracle-based optimization problem formulations. Using this language, we propose a framework that automatically checks whether a user-provided optimization problem fits a known template. Leveraging on an extensive library of optimization methods with their associated convergence rates, the framework allows automatically ranking applicable optimization methods according to their worst-case theoretical guarantees.
Under review With Yassine Kamri, Mehdi Madani and François Glineur, we conduct extensive benchmarking experiments for CH prices computation on a large panel of first-order methods. We then suggest methods combined with heuristics to most efficiently solve CH pricing.
ECC 2023 With Andrea Della Vecchia, Silvia Villa and François Glineur, we propose a kernel SVM solver relying on a Nyström approximation and an accelerated variant of the stochastic subgradient method to solve large-scale kernel SVMs.