论文标题
polyak-lojasiewicz在措施空间和平均野外死亡过程的收敛方面的不平等
Polyak-Łojasiewicz inequality on the space of measures and convergence of mean-field birth-death processes
论文作者
论文摘要
$ \ mathbb {r}^d $中的polyak-lojasiewicz不等式（PLI）是证明梯度下降算法收敛的自然条件。在本文中，我们研究了PLI对概率空间的模拟$ \ Mathcal {p}（\ Mathbb {r}^d）$，并表明它是显示与某些平均野生场相关的一类出生死亡过程的指数收敛的自然条件。我们验证PLI是否为通过KL-Divergence正常的能量功能验证了一系列此类问题。
The Polyak-Lojasiewicz inequality (PLI) in $\mathbb{R}^d$ is a natural condition for proving convergence of gradient descent algorithms. In the present paper, we study an analogue of PLI on the space of probability measures $\mathcal{P}(\mathbb{R}^d)$ and show that it is a natural condition for showing exponential convergence of a class of birth-death processes related to certain mean-field optimization problems. We verify PLI for a broad class of such problems for energy functions regularised by the KL-divergence.
