Optimization with Momentum: Dynamical, Control-Theoretic, and Symplectic Perspectives
(2002.12493)Abstract
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their initial conditions, to provide a simple characterization of convergence rates. In many cases, closed-form expressions are obtained that relate algorithm parameters to the convergence rate. The analysis encompasses discrete time and continuous time, as well as time-invariant and time-variant formulations, and is not limited to a convex or Euclidean setting. In addition, the article rigorously establishes why symplectic discretization schemes are important for momentum-based optimization algorithms, and provides a characterization of algorithms that exhibit accelerated convergence.
We're not able to analyze this paper right now due to high demand.
Please check back later (sorry!).
Generate a summary of this paper on our Pro plan:
We ran into a problem analyzing this paper.