Generalization in Deep Learning

This paper provides theoretical insights into why and how deep learning can generalize well, despite its large capacity, complexity, possible algorithmic instability, nonrobustness, and sharp minima, responding to an open question in the literature. We also discuss approaches to provide non-vacuous generalization guarantees for deep learning. Based on theoretical observations, we propose new open problems and discuss the limitations of our results.Comment: To appear in Mathematics of Deep Learning, Cambridge University Press. All previous results remain unchange

Optimal and Fair Encouragement Policy Evaluation and Learning

In consequential domains, it is often impossible to compel individuals to take treatment, so that optimal policy rules are merely suggestions in the presence of human non-adherence to treatment recommendations. In these same domains, there may be heterogeneity both in who responds in taking-up treatment, and heterogeneity in treatment efficacy. While optimal treatment rules can maximize causal outcomes across the population, access parity constraints or other fairness considerations can be relevant in the case of encouragement. For example, in social services, a persistent puzzle is the gap in take-up of beneficial services among those who may benefit from them the most. When in addition the decision-maker has distributional preferences over both access and average outcomes, the optimal decision rule changes. We study causal identification, statistical variance-reduced estimation, and robust estimation of optimal treatment rules, including under potential violations of positivity. We consider fairness constraints such as demographic parity in treatment take-up, and other constraints, via constrained optimization. Our framework can be extended to handle algorithmic recommendations under an often-reasonable covariate-conditional exclusion restriction, using our robustness checks for lack of positivity in the recommendation. We develop a two-stage algorithm for solving over parametrized policy classes under general constraints to obtain variance-sensitive regret bounds. We illustrate the methods in two case studies based on data from randomized encouragement to enroll in insurance and from pretrial supervised release with electronic monitoring

The Paradox of Noise: An Empirical Study of Noise-Infusion Mechanisms to Improve Generalization, Stability, and Privacy in Federated Learning

In a data-centric era, concerns regarding privacy and ethical data handling grow as machine learning relies more on personal information. This empirical study investigates the privacy, generalization, and stability of deep learning models in the presence of additive noise in federated learning frameworks. Our main objective is to provide strategies to measure the generalization, stability, and privacy-preserving capabilities of these models and further improve them. To this end, five noise infusion mechanisms at varying noise levels within centralized and federated learning settings are explored. As model complexity is a key component of the generalization and stability of deep learning models during training and evaluation, a comparative analysis of three Convolutional Neural Network (CNN) architectures is provided. The paper introduces Signal-to-Noise Ratio (SNR) as a quantitative measure of the trade-off between privacy and training accuracy of noise-infused models, aiming to find the noise level that yields optimal privacy and accuracy. Moreover, the Price of Stability and Price of Anarchy are defined in the context of privacy-preserving deep learning, contributing to the systematic investigation of the noise infusion strategies to enhance privacy without compromising performance. Our research sheds light on the delicate balance between these critical factors, fostering a deeper understanding of the implications of noise-based regularization in machine learning. By leveraging noise as a tool for regularization and privacy enhancement, we aim to contribute to the development of robust, privacy-aware algorithms, ensuring that AI-driven solutions prioritize both utility and privacy

Generalization in Deep Learning

With a direct analysis of neural networks, this paper presents a mathematically tight generalization theory to partially address an open problem regarding the generalization of deep learning. Unlike previous bound-based theory, our main theory is quantitatively as tight as possible for every dataset individually, while producing qualitative insights competitively. Our results give insight into why and how deep learning can generalize well, despite its large capacity, complexity, possible algorithmic instability, nonrobustness, and sharp minima, answering to an open question in the literature. We also discuss limitations of our results and propose additional open problems