The content discusses the theory and applications of the Sum-Of-Squares (SOS) technique, focusing on optimization problems and semidefinite programs. It covers the extension of SOS to infinite-dimensional feature spaces using reproducing kernels, highlighting its utilization in estimating quantities in information theory. The lecture structure includes a discussion on convex duality, the representation of non-negative functions as sums of squares, and the tightness of the approximation. It also explores the application of SOS in optimal control and information theory, specifically the computation of the log partition function and the kernel KL divergence. The connection between optimization, control, and information theory through the SOS technique is emphasized.
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arxiv.org
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by Francis Bach... kl. arxiv.org 03-12-2024
https://arxiv.org/pdf/2306.16255.pdfDybere Forespørgsler