Mirror Descent Algorithms for Minimizing Interacting Free Energy
Mirror Descent Algorithms for Minimizing Interacting Free Energy
复制标题
用于最小化相互作用自由能的镜像下降算法
DOI：
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发表时间：
2020
影响因子：
2.5
通讯作者：
Lexing Ying
中科院分区：
文献类型：
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作者：
Lexing Ying
本文考虑最小化相互作用自由能的问题。受镜像下降算法的启发，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，该度量考虑了参考测量和相互作用项。该度量自然表明概率度量的单调重新参数化。通过使用显式欧拉方法离散化重新参数化的下降动力学，我们得到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。数值结果旨在证明所提出算法的效率。
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.