This project focuses on the development of advanced deep neural network models for decision-making under uncertainty, specifically for learning over networks and graphs. We will create sophisticated methods to continuously learn the parameters of underlying mathematical models as different problem instances are processed. This approach will enable the development of models that do not require a priori data and can improve over time as more data is collected. We will test these models in various real-world applications, including efficient navigation and learning over networks. This project is a continuation of a previous project, with an emphasis on improving sample efficiency to reduce the data required in the learning process. Developing sample-efficient methods is a key aspect of modern machine learning. Improving computational efficiency will be another focus. Additionally, we will explore broader applications and case studies. The requested compute is roughly 400 GPU-h/month with the deviation of 100 hours.