핵심 개념
Sum-Of-Squares technique is a powerful tool for optimization, control, and information theory.
초록
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.
LECTURE 1
Introduction to the Sum-Of-Squares technique for optimization problems.
Application of SOS in estimating quantities in information theory.
LECTURE 2
Application of SOS in optimal control and reinforcement learning.
Use of SOS relaxation in solving the Hamilton-Jacobi-Bellman equation.
LECTURE 3
Extension of SOS to information theory, focusing on the log partition function.
Discussion on the kernel KL divergence and its properties.
통계
"The Sum-of-Squares (SOS) approximation method is a technique used in optimization problems."
"The catch is that we are imposing constraints over a dense set."
"The representation of h associated with H is not unique."
"The number of squares in the SOS decomposition will be equal to the rank of the matrix H."
"The linear span V plays a key role in the SOS construction."
인용구
"The Sum-of-Squares (SOS) approximation method is a technique used in optimization problems."
"The representation of h associated with H is not unique."