We introduce a gradient-based learning method to automatically adapt Markov chain Monte Carlo (MCMC) proposal distributions to intractable targets. We define a maximum entropy regularised objective function, referred to as generalised speed measure, which can be robustly optimised over the parameters of the proposal distribution by applying stochastic gradient optimisation. An advantage of our method compared to traditional adaptive MCMC methods is that the adaptation occurs even when candidate state values are rejected. This is a highly desirable property of any adaptation strategy because the adaptation starts in early iterations even if the initial proposal distribution is far from optimum. We apply the framework for learning multivariate random walk Metropolis and Metropolis-adjusted Langevin proposals with full covariance matrices, and provide empirical evidence that our method can outperform other MCMC algorithms, including Hamiltonian Monte Carlo schemes.

本研究提出使用基于梯度的学习方法来自适应马尔可夫链蒙特卡罗（MCMC）提议分布，应用随机梯度优化能通过定义的最大熵正则化目标函数来优化提议分布的参数，并证明相比传统自适应MCMC方法，该方法带有更高的性能；并应用于多元随机步长Metropolis和Metropolis-adjusted Langevin提议与完整协方差矩阵，并证实该方法在MCMC算法中表现优异，包括哈密顿蒙特卡罗方案。

基于梯度的自适应马尔科夫链蒙特卡罗