Jana Lepšová

Andrii Kliachkin, Jana Lepšová, Gilles Bareilles et al.

The ability to train Deep Neural Networks (DNNs) with constraints is instrumental in improving the fairness of modern machine-learning models. Many algorithms have been analysed in recent years, and yet there is no standard, widely accepted method for the constrained training of DNNs. In this paper, we provide a challenging benchmark of real-world large-scale fairness-constrained learning tasks, built on top of the US Census (Folktables). We point out the theoretical challenges of such tasks and review the main approaches in stochastic approximation algorithms. Finally, we demonstrate the use of the benchmark by implementing and comparing three recently proposed, but as-of-yet unimplemented, algorithms both in terms of optimization performance, and fairness improvement. We release the code of the benchmark as a Python package at https://github.com/humancompatible/train.

Adam Bosák, Andrii Kliachkin, Jana Lepšová et al.

Constrained machine learning enables fairness-aware training, physics-informed neural networks, and integration of symbolic domain knowledge into statistical models. Despite its practical importance, no general method exists for the non-convex, non-smooth, stochastic setting that arises naturally in deep learning. We propose the Stochastic Penalty-Barrier Method (SPBM), which extends classical penalty and barrier methods to this setting via exponential dual averaging, a~stabilized penalty schedule, and the Moreau envelope to handle non-smoothness. Experiments across multiple settings show that SPBM matches or outperforms existing constrained optimization baselines while incurring only linear runtime overhead compared to unconstrained Adam for up to 10,000 constraints.

Gilles Bareilles, Allen Gehret, Johannes Aspman et al.

One can see deep-learning models as compositions of functions within the so-called tame geometry. In this expository note, we give an overview of some topics at the interface of tame geometry (also known as o-minimality), optimization theory, and deep learning theory and practice. To do so, we gradually introduce the concepts and tools used to build convergence guarantees for stochastic gradient descent in a general nonsmooth nonconvex, but tame, setting. This illustrates some ways in which tame geometry is a natural mathematical framework for the study of AI systems, especially within Deep Learning.