MATH Seminar

Title: Inference, Computation, and Games
Seminar: Numerical Analysis and Scientific Computing
Speaker: Florian Schaefer of Georgia Institute of Technology
Contact: Yuanzhe Xi,
Date: 2021-09-24 at 12:30PM
Venue: MSC W201
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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, and computer graphics.

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.

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