Games for Computation and Learning

This project had two main objectives for methods emerging at the interface be-tween game theory, uncertainty quantication, and numerical approximation (I) their continued application to high impact problems of practical importance in computational mathematics (II) their development towards machine learning. With this purpose and a dual emphasis on conceptual/theoretical advancements and algorithmic/computational complexity advancements the accomplishments of this program are as follows. (1) We have developed general robust methods for learning kernels through (a) hyperparameter tuning via Kernel Flows (a variant of cross-validation) with applications to learning dynamical systems and to the extrapolation of weather time series, and (b) programming kernels through interpretable regression networks (kernel mode decomposition) with applications to empirical mode decomposition.(2) We have discovered a very robust and massively parallel algorithm, based on Kullback-Liebler divergence (KL) minimization that computes accurate approximations of the inverse Cholesky factors of dense kernel matrices with rigorous a priori O(N log(N) log2d(N/) complexity vs. accuracy guarantees