Seminar Details
2025-10-14 (14:00) : Newcomers seminars (PhDs)
At Euler building (room a.002)
Organized by Mathematical Engineering
Section 1: Low-rank PSD matrix completion
Speaker :
Sophie Lequeu (PhD UCLouvain/INMA)
Abstract :
While convexity is traditionally seen as essential for solving optimization problems, many nonconvex ones pose no significant issues in practice. Moreover, simpler nonconvex formulations are generally more compact and amenable to parallel solving, even when an equivalent convex formulation exists. This justifies the interest in studying the global landscape of selected optimization problems, in order to determine the characteristics that distinguish problems with benign nonconvexity from those with non-benign nonconvexity.
In this research project, we will study the Burer–Monteiro nonconvex reformulation of the low-rank PSD matrix completion problem. For sparsity patterns corresponding to chordal graphs, a classical result guarantees the existence of a low-rank solution, encouraging the use of this reformulation. The goal is to determine conditions under which this formulation has no spurious local minima, by studying characteristics of the sparsity pattern.
Section 2: Novel deep learning architectures for the detection of the stochastic gravitational wave background.
Speaker :
Antonin Oswald (PhD UCLouvain/INMA)
Abstract :
We propose to advance the understanding of the stochastic gravitational wave background by proposing new machine learning architectures specifically dedicated to processing correlation matrices signal representations. These architectures will heavily rely on the geometry of the manifold of positive-definite matrices, to which the correlation matrices representing classically the signal rely. We will explore several directions, aiming to account for time- and frequency dependency in the correlation representations. We will then use our proposed novel architectures for denoising correlation matrices in view of subsequent SGWB detection.
Section 3: Path-complete reinforcement learning
Speaker :
Lea Ninite (PhD UCLouvain/INMA)
Abstract :
Reinforcement Learning (RL) has achieved remarkable success in complex control tasks, yet its lack of theoretical guarantees limits its use in safety-critical systems. In RL, the Q-function satisfies a decrease condition similar to that of a Lyapunov function, but this relation is typically enforced through heuristic, data-driven updates, which hinders robustness and interpretability. In contrast, Path-Complete Lyapunov Functions (PCLFs) offer a systematic and combinatorial framework for encoding stability through sets of local decrease conditions on a graph structure.
This PhD project aims to bridge these two paradigms by developing a Path-Complete Reinforcement Learning (PCRL) framework, introducing a path-complete relaxation of the Bellman equation. As a first step, we focus on computing an upper bound of the value function for arbitrarily switched linear systems using path-complete graphs, where each node encodes a quadratic function satisfying Bellman-like inequalities. Preliminary results show that this construction can yield tight upper bounds on the true value function, highlighting the potential of path-complete methods to bring theoretical structure to learning-based control.