Mirror Descent Algorithms for Minimizing Interacting Free Energy

Lexing Ying

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arXiv · 2004.04555

Mirror Descent Algorithms for Minimizing Interacting Free Energy

Lexing Ying

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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.

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Lexing Ying. 2020-04-08. Mirror Descent Algorithms for Minimizing Interacting Free Energy. https://arxiv.org/abs/2004.04555

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