Mirror Descent Algorithms for Minimizing Interacting Free Energy
Optimization and Control
2020-04-10 v1 Machine Learning
Numerical Analysis
Numerical Analysis
Abstract
This note considers the problem of minimizing interacting free energy. Motivated by the mirror descent algorithm, for a given interacting free energy, we propose a descent dynamics with a novel metric that takes into consideration the reference measure and the interacting term. This metric naturally suggests a monotone reparameterization of the probability measure. By discretizing the reparameterized descent dynamics with the explicit Euler method, we arrive at a new mirror-descent-type algorithm for minimizing interacting free energy. Numerical results are included to demonstrate the efficiency of the proposed algorithms.
Cite
@article{arxiv.2004.04555,
title = {Mirror Descent Algorithms for Minimizing Interacting Free Energy},
author = {Lexing Ying},
journal= {arXiv preprint arXiv:2004.04555},
year = {2020}
}