In the second part, we show that the conditional near-independence properties of smooth Gaussian processes imply the near-sparsity of Cholesky factors of their dense covariance matrices. We use this insight to derive simple, fast solvers with state-of-the-art complexity vs. accuracy guarantees for general elliptic differential and integral equations. Our methods come with rigorous error estimates, are easy to parallelize, and show good performance in practice.
Friday, April 22, 2022 - 2:00pm
Florian T Schaefer
Abstract: In this talk, we develop algorithms for numerical computation, based on ideas from competitive games and statistical inference.
In the first part, we propose competitive gradient descent (CGD) as a natural generalization of gradient descent to saddle point problems and general sum games. Whereas gradient descent minimizes a local linear approximation at each step, CGD uses the Nash equilibrium of a local bilinear approximation. Explicitly accounting for agent-interaction significantly improves the convergence properties, as demonstrated in applications to GANs, reinforcement learning, computer graphics, and physics-informed neural networks.
Bio: Florian Schäfer is an assistant professor in the School of Computational Science and Engineering at Georgia Tech. Prior to joining Georgia Tech, he received his PhD in applied and computational mathematics at Caltech, working with Houman Owhadi. Before that, he received Bachelor’s and Master’s degrees in Mathematics at the University of Bonn. His research interests lie at the interface of numerical computation, statistical inference, and competitive games.