Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamics

作     者：Zhang, Benjamin J. Marzouk, Youssef M. Spiliopoulos, Konstantinos 

作者机构：MIT Ctr Computat Sci & Engn Dept Aeronaut & Astronaut Cambridge MA 02139 USA Boston Univ Dept Math & Stat Boston MA 02215 USA 

出 版 物：《STATISTICS AND COMPUTING》 (统计学与计算)

年 卷 期：2022年第32卷第5期

页      面：78-78页

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Air Force Office of Scientific Research, Analysis and Synthesis of Rare Events (ANSRE) MURI National Science Foundation [DMS 1550918, DMS 2107856] Simons Foundation 

主　　题：Monte Carlo sampling Stochastic gradient Langevin dynamics Riemannian manifold Langevin dynamics Geometry-informed irreversibility Bayesian computation 

摘      要：We introduce a novel geometry-informed irreversible perturbation that accelerates convergence of the Langevin algorithm for Bayesian computation. It is well documented that there exist perturbations to the Langevin dynamics that preserve its invariant measure while accelerating its convergence. Irreversible perturbations and reversible perturbations (such as Riemannian manifold Langevin dynamics (RMLD)) have separately been shown to improve the performance of Langevin samplers. We consider these two perturbations simultaneously by presenting a novel form of irreversible perturbation for RMLD that is informed by the underlying geometry. Through numerical examples, we show that this new irreversible perturbation can improve estimation performance over irreversible perturbations that do not take the geometry into account. Moreover we demonstrate that irreversible perturbations generally can be implemented in conjunction with the stochastic gradient version of the Langevin algorithm. Lastly, while continuous-time irreversible perturbations cannot impair the performance of a Langevin estimator, the situation can sometimes be more complicated when discretization is considered. To this end, we describe a discrete-time example in which irreversibility increases both the bias and variance of the resulting estimator.