Adversarial games in machine learning : challenges and applications

L’apprentissage automatique repose pour un bon nombre de problèmes sur la minimisation d’une fonction de coût, pour ce faire il tire parti de la vaste littérature sur l’optimisation qui fournit des algorithmes et des garanties de convergences pour ce type de problèmes. Cependant récemment plusieurs modèles d’apprentissage automatique qui ne peuvent pas être formulé comme la minimisation d’un coût unique ont été propose, à la place ils nécessitent de définir un jeu entre plusieurs joueurs qui ont chaque leur propre objectif. Un de ces modèles sont les réseaux antagonistes génératifs (GANs). Ce modèle génératif formule un jeu entre deux réseaux de neurones, un générateur et un discriminateur, en essayant de tromper le discriminateur qui essaye de distinguer les vraies images des fausses, le générateur et le discriminateur s’améliore résultant en un équilibre de Nash, ou les images produites par le générateur sont indistinguable des vraies images. Malgré leur succès les GANs restent difficiles à entrainer à cause de la nature antagoniste du jeu, nécessitant de choisir les bons hyperparamètres et résultant souvent en une dynamique d’entrainement instable. Plusieurs techniques de régularisations ont été propose afin de stabiliser l’entrainement, dans cette thèse nous abordons ces instabilités sous l’angle d’un problème d’optimisation. Nous commençons par combler le fossé entre la littérature d’optimisation et les GANs, pour ce faire nous formulons GANs comme un problème d’inéquation variationnelle, et proposons de la littérature sur le sujet pour proposer des algorithmes qui convergent plus rapidement. Afin de mieux comprendre quels sont les défis de l’optimisation des jeux, nous proposons plusieurs outils afin d’analyser le paysage d’optimisation des GANs. En utilisant ces outils, nous montrons que des composantes rotationnelles sont présentes dans le voisinage des équilibres, nous observons également que les GANs convergent rarement vers un équilibre de Nash mais converge plutôt vers des équilibres stables locaux (LSSP). Inspirer par le succès des GANs nous proposons pour finir, une nouvelle famille de jeux que nous appelons adversarial example games qui consiste à entrainer simultanément un générateur et un critique, le générateur cherchant à perturber les exemples afin d’induire en erreur le critique, le critique cherchant à être robuste aux perturbations. Nous montrons qu’à l’équilibre de ce jeu, le générateur est capable de générer des perturbations qui transfèrent à toute une famille de modèles.Many machine learning (ML) problems can be formulated as minimization problems, with a large optimization literature that provides algorithms and guarantees to solve this type of problems. However, recently some ML problems have been proposed that cannot be formulated as minimization problems but instead require to define a game between several players where each player has a different objective. A successful application of such games in ML are generative adversarial networks (GANs), where generative modeling is formulated as a game between a generator and a discriminator, where the goal of the generator is to fool the discriminator, while the discriminator tries to distinguish between fake and real samples. However due to the adversarial nature of the game, GANs are notoriously hard to train, requiring careful fine-tuning of the hyper-parameters and leading to unstable training. While regularization techniques have been proposed to stabilize training, we propose in this thesis to look at these instabilities from an optimization perspective. We start by bridging the gap between the machine learning and optimization literature by casting GANs as an instance of the Variational Inequality Problem (VIP), and leverage the large literature on VIP to derive more efficient and stable algorithms to train GANs. To better understand what are the challenges of training GANs, we then propose tools to study the optimization landscape of GANs. Using these tools we show that GANs do suffer from rotation around their equilibrium, and that they do not converge to Nash-Equilibria. Finally inspired by the success of GANs to generate images, we propose a new type of games called Adversarial Example Games that are able to generate adversarial examples that transfer across different models and architectures

Stochastic Gradient Descent-Ascent: Unified Theory and New Efficient Methods

Stochastic Gradient Descent-Ascent (SGDA) is one of the most prominent algorithms for solving min-max optimization and variational inequalities problems (VIP) appearing in various machine learning tasks. The success of the method led to several advanced extensions of the classical SGDA, including variants with arbitrary sampling, variance reduction, coordinate randomization, and distributed variants with compression, which were extensively studied in the literature, especially during the last few years. In this paper, we propose a unified convergence analysis that covers a large variety of stochastic gradient descent-ascent methods, which so far have required different intuitions, have different applications and have been developed separately in various communities. A key to our unified framework is a parametric assumption on the stochastic estimates. Via our general theoretical framework, we either recover the sharpest known rates for the known special cases or tighten them. Moreover, to illustrate the flexibility of our approach we develop several new variants of SGDA such as a new variance-reduced method (L-SVRGDA), new distributed methods with compression (QSGDA, DIANA-SGDA, VR-DIANA-SGDA), and a new method with coordinate randomization (SEGA-SGDA). Although variants of the new methods are known for solving minimization problems, they were never considered or analyzed for solving min-max problems and VIPs. We also demonstrate the most important properties of the new methods through extensive numerical experiments.Comment: 72 pages, 4 figures, 3 tables. Changes in v2: new results were added (Theorem 2.5 and its corollaries), few typos were fixed, more clarifications were added. Code: https://github.com/hugobb/sgd

The quick motor function test: a new tool to rate clinical severity and motor function in Pompe patients

Pompe disease is a lysosomal storage disorder characterized by progressive muscle weakness. With the emergence of new treatment options, psychometrically robust outcome measures are needed to monitor patients’ clinical status. We constructed a motor function test that is easy and quick to use. The Quick Motor Function Test (QMFT) was constructed on the basis of the clinical expertise of several physicians involved in the care of Pompe patients; the Gross Motor Function Measure and the IPA/Erasmus MC Pompe survey. The test comprises 16 items. Validity and test reliability were determined in a cohort of 91 Pompe patients (5 to 76 years of age). In addition, responsiveness of the scale to changes in clinical condition over time was examined in a subgroup of 18 patients receiving treatment and 23 untreated patients. Interrater and intrarater reliabilities were good (intraclass correlation coefficients: 0.78 to 0.98 and 0.76 to 0.98). The test correlated strongly with proximal muscle strength assessed by hand held dynamometry and manual muscle testing (rs= 0.81, rs=0.89), and showed significant differences between patient groups with different disease severities. A clinical-empirical exploration to assess responsiveness showed promising results, albeit it should be repeated in a larger group of patients. In conclusion, the Quick Motor Function Test can reliably rate clinical severity and motor function in children and adults with Pompe disease

Changes in preterm birth and stillbirth during COVID-19 lockdowns in 26 countries.

Preterm birth (PTB) is the leading cause of infant mortality worldwide. Changes in PTB rates, ranging from -90% to +30%, were reported in many countries following early COVID-19 pandemic response measures ('lockdowns'). It is unclear whether this variation reflects real differences in lockdown impacts, or perhaps differences in stillbirth rates and/or study designs. Here we present interrupted time series and meta-analyses using harmonized data from 52 million births in 26 countries, 18 of which had representative population-based data, with overall PTB rates ranging from 6% to 12% and stillbirth ranging from 2.5 to 10.5 per 1,000 births. We show small reductions in PTB in the first (odds ratio 0.96, 95% confidence interval 0.95-0.98, P value <0.0001), second (0.96, 0.92-0.99, 0.03) and third (0.97, 0.94-1.00, 0.09) months of lockdown, but not in the fourth month of lockdown (0.99, 0.96-1.01, 0.34), although there were some between-country differences after the first month. For high-income countries in this study, we did not observe an association between lockdown and stillbirths in the second (1.00, 0.88-1.14, 0.98), third (0.99, 0.88-1.12, 0.89) and fourth (1.01, 0.87-1.18, 0.86) months of lockdown, although we have imprecise estimates due to stillbirths being a relatively rare event. We did, however, find evidence of increased risk of stillbirth in the first month of lockdown in high-income countries (1.14, 1.02-1.29, 0.02) and, in Brazil, we found evidence for an association between lockdown and stillbirth in the second (1.09, 1.03-1.15, 0.002), third (1.10, 1.03-1.17, 0.003) and fourth (1.12, 1.05-1.19, <0.001) months of lockdown. With an estimated 14.8 million PTB annually worldwide, the modest reductions observed during early pandemic lockdowns translate into large numbers of PTB averted globally and warrant further research into causal pathways