Algorithmic Uncertainty Quantification for Learning and Decision Making

Objective

Assessing the uncertainty of predictions of modern large-scale machine learning systems is crucial for understanding their limitations and the quality of solutions they provide, especially so when these systems are used for making decisions in the real world. Motivated by this need, this project addresses a variety of questions of uncertainty quantification and develops new methods for deriving statistical guarantees on the accuracy of outputs of ML systems. Our methodology is inspired by an emerging line of work we call algorithmic statistics, which uses tools from the theory of algorithms to prove complex statistical statements. We propose to extend these techniques to the more challenging domain of analyzing modern large-scale machine learning systems, and develop a theory of Algorithmic Uncertainty Quantification. Using the newly developed tools, we will address diverse statistical tasks such as bounding the generalization error of machine learning algorithms, estimating the parameters of large nonlinear statistical models, or designing provably efficient algorithms for interactive decision-making problems. The results will significantly advance the state of the art in well-studied areas of research such as statistical learning theory and reinforcement learning, not only by providing new tools for the analysis of existing algorithms and architectures but also by inspiring new principles for the development of the next generation of ML systems.