arXiv subjects

Thomas Boudou

Publications and source records attributed to Thomas Boudou.

5 recordsLinked to original sources

arXiv2026

Unveiling the Non-Monotonic Effect of Privacy on Generalization under Byzantine Robustness

Recent work has established a fundamental trilemma between Byzantine robustness, local differential privacy (LDP), and optimization error in distributed learning. We show that this trilemma does not universally extend to generalization error, but instead depends critically on the privacy regime. Specifically, in the high-noise regime (strong privacy), we prove that increasing privacy reduces the generalization error, i.e., there is no tension between robustness and privacy. In the low-noise regime (weaker privacy), however, the tension between robustness and privacy reappears and increasing privacy indeed degrades generalization. Our theory explains this surprising non-monotonic behavior of the generalization error via matching lower and upper bounds on the algorithmic stability of Byzantine-robust distributed learning under LDP constraints. We corroborate and further analyze these theoretical findings with empirical evaluations.

cs.LG↗

arXiv2026

Dangerous Liaisons of Convex Learning and Non-Affine Aggregation

Last-iterate convergence and generalization guarantees in first-order convex learning hinge on the monotonicity of the update operator. While linear averaging preserves the monotonicity of gradient updates, this property is often violated when gradients are aggregated non-affinely, as in modern pipelines enforcing constraints like adaptivity, privacy, robustness or fairness. Whether it is possible to design non-affine aggregation rules that maintain monotonicity has remained an open question. We answer this question negatively: we prove that the monotonicity of aggregated gradients is preserved if and only if the aggregation rule is positively affine. Consequently, non-affine aggregation prevents steady convergence and substantially degrade algorithmic stability. We quantify these drawbacks and propose a path forward by identifying sufficient conditions under which monotonicity can be restored. Our results provide a unified theoretical framework explaining the disparate failure modes observed in modern learning systems.

cs.LG↗

arXiv2026

Optimal Transport under Group Fairness Constraints

Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two individuals from any two given groups in the OT plan satisfies a predefined target. We first propose a modified Sinkhorn algorithm to compute perfectly fair transport plans efficiently. Since exact fairness can significantly degrade matching quality in practice, we then develop two relaxation strategies. The first one involves solving a penalized OT problem, for which we derive novel finite-sample complexity guarantees. Our second strategy leverages bilevel optimization to learn a ground cost that induces a fair OT solution, and we establish a bound on the deviation of fairness when matching unseen data. Finally, we present empirical results illustrating the performance of our approaches and the trade-off between fairness and transport cost.

stat.ML↗

arXiv2025

Tight Stability Bounds for Robust Distributed Learning: Byzantine Failures Hurt Generalization More than Data Poisoning

Robust distributed learning algorithms aim to maintain reliable performance despite the presence of misbehaving workers. Such misbehaviors are commonly modeled as \textit{Byzantine failures}, allowing arbitrarily corrupted communication, or as \textit{data poisoning}, a weaker form of corruption restricted to local training data. While prior work shows similar optimization guarantees for both models, an important question remains: \textit{How do these threat models impact generalization?} We show, for the first time, a fundamental gap in generalization guarantees between the two threat models: Byzantine failures yield strictly worse rates than those achievable under data poisoning. Our findings are based upon a tight algorithmic stability analysis of robust distributed learning. Specifically, with $f$ out of $n$ workers misbehaving, we prove that: \textit{(i)} under data poisoning, the uniform algorithmic stability of a robust distributed learning algorithm

cs.LG↗

arXiv2009

In vivo measurement of human brain elasticity using a light aspiration device

The brain deformation that occurs during neurosurgery is a serious issue impacting the patient "safety" as well as the invasiveness of the brain surgery. Model-driven compensation is a realistic and efficient solution to solve this problem. However, a vital issue is the lack of reliable and easily obtainable patient-specific mechanical characteristics of the brain which, according to clinicians' experience, can vary considerably. We designed an aspiration device that is able to meet the very rigorous sterilization and handling process imposed during surgery, and especially neurosurgery. The device, which has no electronic component, is simple, light and can be considered as an ancillary instrument. The deformation of the aspirated tissue is imaged via a mirror using an external camera. This paper describes the experimental setup as well as its use during a specific neurosurgery. The experimental data was used to calibrate a continuous model. We show that we were able to extract an in vivo constitutive law of the brain elasticity: thus for the first time, measurements are carried out per-operatively on the patient, just before the resection of the brain parenchyma. This paper discloses the results of a difficult experiment and provide for the first time in-vivo data on human brain elasticity. The results point out the softness as well as the highly non-linear behavior of the brain tissue.

physics.med-ph↗