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.

中文翻译：

---

用于最小化相互作用自由能的镜像下降算法

本说明考虑了使相互作用的自由能最小化的问题。受镜像下降算法的激励，对于给定的相互作用自由能，我们提出了一种具有新颖度量的下降动力学，该度量考虑了参考度量和相互作用项。该度量标准自然暗示了概率度量的单调重新参数化。通过使用显式Euler方法离散化重新参数化的下降动力学，我们得出了一种新的镜像下降型算法，用于最小化相互作用的自由能。数值结果被包括来证明所提出算法的效率。