# Mirror Descent Algorithms for Minimizing Interacting Free Energy

arXiv: https://arxiv.org/abs/2004.04555 · HTML: https://mlsanity.com/paper/2004.04555/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2020.

## Built on by (most cited first, 3 of 3)

- [Convex Analysis of the Mean Field Langevin Dynamics](https://mlsanity.com/paper/2201.10469/) (2022)
- [A connection between Tempering and Entropic Mirror Descent](https://mlsanity.com/paper/2310.11914/) (2023)
- [Approximate Newton policy gradient algorithms](https://mlsanity.com/paper/2110.02398/) (2021)

## Abstract (arXiv)

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.