论文标题
镜像下降算法，以最大程度地减少相互作用的自由能
Mirror Descent Algorithms for Minimizing Interacting Free Energy
论文作者
论文摘要
本说明考虑了最大程度地减少相互作用的自由能的问题。由镜下下降算法激励，对于给定的相互作用的自由能，我们提出了一种带有新型度量的下降动力学，该指标考虑参考度量和相互作用项。该度量自然表明概率度量的单调重聚。通过使用显式Euler方法离散重新聚集的下降动力学，我们到达了一种新的镜像散发型算法，以最大程度地减少相互作用的自由能。包括数值结果以证明所提出的算法的效率。
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.
