Adaptive Non-reversible Stochastic Gradient Langevin Dynamics
This work addresses convergence bottlenecks in stochastic gradient methods for Bayesian inference, offering an incremental improvement over existing non-reversible Langevin dynamics.
The paper tackles the problem of improving convergence rates in Langevin dynamics by adaptively optimizing a skew-symmetric matrix, resulting in a non-reversible diffusion algorithm with enhanced performance, as demonstrated numerically in Bayesian learning and tracking examples.
It is well known that adding any skew symmetric matrix to the gradient of Langevin dynamics algorithm results in a non-reversible diffusion with improved convergence rate. This paper presents a gradient algorithm to adaptively optimize the choice of the skew symmetric matrix. The resulting algorithm involves a non-reversible diffusion algorithm cross coupled with a stochastic gradient algorithm that adapts the skew symmetric matrix. The algorithm uses the same data as the classical Langevin algorithm. A weak convergence proof is given for the optimality of the choice of the skew symmetric matrix. The improved convergence rate of the algorithm is illustrated numerically in Bayesian learning and tracking examples.