Analysis of Kinetic Models for Label Switching and Stochastic Gradient Descent
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Abstract (arXiv)
In this paper we provide a novel approach to the analysis of kinetic models for label switching, which are used for particle systems that can randomly switch between gradient flows in different energy landscapes. Besides problems in biology and physics, we also demonstrate that stochastic gradient descent, the most popular technique in machine learning, can be understood in this setting, when considering a time-continuous variant. Our analysis is focusing on the case of evolution in a collection of external potentials, for which we provide analytical and numerical results about the evolution as well as the stationary problem.
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References · 5
- 2018Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundationscited by 109
- 2021Stochastic gradient descent with noise of machine learning type. Part I: Discrete time analysiscited by 38
- 2020Analysis of Stochastic Gradient Descent in Continuous Timecited by 24
- 2019Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximationcited by 14
- 2021The convergence of the Stochastic Gradient Descent (SGD) : a self-contained proofcited by 9
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