We propose a new approach to unbiased estimation of the gradients of the stationary means associated with parametrized families of Markov chains. Our estimators are particularly efficient when the Markov chains have slow mixing rate. Our approach does not require a specific parametrization except for an oracle to evaluate the transition density and its gradient at a given data point without any additional knowledge about the density function itself. It makes our estimator suitable for parametrizations associated with neural networks. The estimator can potentially achieve large improvement in terms of efficiency. Numerical experiments confirm the good performance predicted by the theory.

翻译：我们提出了一种新方法，用于对参数化马尔可夫链族关联的稳态均值梯度进行无偏估计。当马尔可夫链具有缓慢混合速率时，我们的估计器尤为高效。该方法无需特定参数化形式，仅需一个预言机来评估给定数据点处的转移密度及其梯度，而无需了解密度函数本身的任何额外信息。这使得我们的估计器适用于与神经网络相关的参数化形式。该估计器在效率方面有望实现显著提升。数值实验验证了理论所预测的优良性能。