论文标题
自适应非可逆随机梯度Langevin动力学
Adaptive Non-reversible Stochastic Gradient Langevin Dynamics
论文作者
论文摘要
众所周知，将任何偏斜的对称矩阵添加到Langevin Dynamics算法的梯度中会导致不可逆转的扩散，并提高收敛速率。本文提出了一种梯度算法，以适应优化偏斜对称矩阵的选择。所得算法涉及一种非可逆性扩散算法交叉与随机梯度算法相结合的，可适应偏斜的对称矩阵。该算法使用与经典Langevin算法相同的数据。为偏斜对称矩阵的选择提供了弱收敛的证明。在贝叶斯学习和跟踪示例中，用数字说明了算法的收敛速率的提高。
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.
