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The Physical Systems Behind Optimization Algorithms
Lin Yang · Raman Arora · Vladimir Braverman · Tuo Zhao

Wed Dec 05 02:00 PM -- 04:00 PM (PST) @ Room 210 #85

We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient descent, coordinate gradient descent, proximal coordinate gradient, and Newton's methods as well as their Nesterov's accelerated variants in a unified framework motivated by a natural connection of optimization algorithms to physical systems. Our analysis is applicable to more general algorithms and optimization problems {\it \textbf{beyond}} convexity and strong convexity, e.g. Polyak-\L ojasiewicz and error bound conditions (possibly nonconvex).

Author Information

Lin Yang (Princeton University)
Raman Arora (Johns Hopkins University)
Vladimir Braverman (Johns Hopkins University)
Tuo Zhao (Georgia Tech)

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