Modern machine learning systems perform well when training and deployment data follow the same distribution, yet they often fail under distribution shift, noise, or adversarial perturbations—an especially serious limitation in high-stakes applications such as medicine. This project develops a principled and scalable foundation for robust machine learning by formulating training as a minimax problem. The central idea is to cast robustness within a unified minimax framework, where learning optimizes performance against worst-case distributions drawn from structured uncertainty sets. This formulation encompasses causality, distributionally robust optimization, and adversarial training within a single framework, with a particular focus on nonlinear models and large-scale settings. The project pursues three complementary aims: establishing robust training using minimax, developing the analysis for nonlinear models using kernel methods and deep networks, and proposing computationally efficient algorithms for large-scale robust learning through tractable reformulations of minimax objectives. By unifying robustness paradigms, providing nonlinear analysis, and developing scalable optimization methods, the project delivers principled and practical approaches to reliable machine learning, with direct relevance to real-world applications such as biomedical signal analysis and to trustworthy, mathematically grounded AI. The main supervisor for the doctoral student in this project will be Antônio H. Ribeiro from Department of Information Technology, Uppsala University.