Adaptively Preconditioned Stochastic Gradient Langevin Dynamics
This work addresses convergence and generalization issues in deep learning optimization for researchers and practitioners, representing an incremental improvement over existing preconditioning methods.
The paper tackled the problem of poor scaling in Stochastic Gradient Langevin Dynamics (SGLD) due to isotropic noise by proposing an adaptive preconditioning method, achieving convergence speeds comparable to adaptive first-order methods like Adam and AdaGrad while matching SGD's generalization performance on test sets.
Stochastic Gradient Langevin Dynamics infuses isotropic gradient noise to SGD to help navigate pathological curvature in the loss landscape for deep networks. Isotropic nature of the noise leads to poor scaling, and adaptive methods based on higher order curvature information such as Fisher Scoring have been proposed to precondition the noise in order to achieve better convergence. In this paper, we describe an adaptive method to estimate the parameters of the noise and conduct experiments on well-known model architectures to show that the adaptively preconditioned SGLD method achieves convergence with the speed of adaptive first order methods such as Adam, AdaGrad etc. and achieves generalization equivalent of SGD in the test set.