Methods for integrating machine learning and constrained optimization

In the framework of industrial problems, the application of Constrained Optimization is known to have overall very good modeling capability and performance and stands as one of the most powerful, explored, and exploited tool to address prescriptive tasks. The number of applications is huge, ranging from logistics to transportation, packing, production, telecommunication, scheduling, and much more. The main reason behind this success is to be found in the remarkable effort put in the last decades by the OR community to develop realistic models and devise exact or approximate methods to solve the largest variety of constrained or combinatorial optimization problems, together with the spread of computational power and easily accessible OR software and resources. On the other hand, the technological advancements lead to a data wealth never seen before and increasingly push towards methods able to extract useful knowledge from them; among the data-driven methods, Machine Learning techniques appear to be one of the most promising, thanks to its successes in domains like Image Recognition, Natural Language Processes and playing games, but also the amount of research involved. The purpose of the present research is to study how Machine Learning and Constrained Optimization can be used together to achieve systems able to leverage the strengths of both methods: this would open the way to exploiting decades of research on resolution techniques for COPs and constructing models able to adapt and learn from available data. In the first part of this work, we survey the existing techniques and classify them according to the type, method, or scope of the integration; subsequently, we introduce a novel and general algorithm devised to inject knowledge into learning models through constraints, Moving Target. In the last part of the thesis, two applications stemming from real-world projects and done in collaboration with Optit will be presented.

Concepts and methods for efficient decentralized learning in federated settings

Deep Neural Networks (DNNs) have revolutionized a wide range of applications beyond traditional machine learning and artificial intelligence fields, e.g., computer vision, healthcare, natural language processing and others. At the same time, edge devices have become central in our society, generating an unprecedented amount of data which could be used to train data-hungry models such as DNNs. However, the potentially sensitive or confidential nature of gathered data poses privacy concerns when storing and processing them in centralized locations. To this purpose, decentralized learning decouples model training from the need of directly accessing raw data, by alternating on-device training and periodic communications. The ability of distilling knowledge from decentralized data, however, comes at the cost of facing more challenging learning settings, such as coping with heterogeneous hardware and network connectivity, statistical diversity of data, and ensuring verifiable privacy guarantees. This Thesis proposes an extensive overview of decentralized learning literature, including a novel taxonomy and a detailed description of the most relevant system-level contributions in the related literature for privacy, communication efficiency, data and system heterogeneity, and poisoning defense. Next, this Thesis presents the design of an original solution to tackle communication efficiency and system heterogeneity, and empirically evaluates it on federated settings. For communication efficiency, an original method, specifically designed for Convolutional Neural Networks, is also described and evaluated against the state-of-the-art. Furthermore, this Thesis provides an in-depth review of recently proposed methods to tackle the performance degradation introduced by data heterogeneity, followed by empirical evaluations on challenging data distributions, highlighting strengths and possible weaknesses of the considered solutions. Finally, this Thesis presents a novel perspective on the usage of Knowledge Distillation as a mean for optimizing decentralized learning systems in settings characterized by data heterogeneity or system heterogeneity. Our vision on relevant future research directions close the manuscript.