Adaptive Stochastic Gradient Langevin Dynamics: Taming Convergence and Saddle Point Escape Time
In this paper, we propose a new adaptive stochastic gradient Langevin dynamics (ASGLD) algorithmic framework and its two specialized versions, namely adaptive stochastic gradient (ASG) and adaptive gradient Langevin dynamics(AGLD), for non-convex optimization problems. All proposed algorithms can escape from saddle points with at most $O(\log d)$ iterations, which is nearly dimension-free. Further, we show that ASGLD and ASG converge to a local minimum with at most $O(\log d/\epsilon^4)$ iterations. Also, ASGLD with full gradients or ASGLD with a slowly linearly increasing batch size converge to a local minimum with iterations bounded by $O(\log d/\epsilon^2)$, which outperforms existing first-order methods.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Taming neural networks with TUSLA: Non-convex learning via adaptive stochastic gradient Langevin algorithms
Artificial neural networks (ANNs) are typically highly nonlinear systems which are finely tuned via the optimization of their associated, non-convex loss functions. In many cases, the gradient of any such loss function h…
RELTA-SGLD: Relative-Growth Localized Taming for Nonconvex Stochastic-Gradient Langevin Learning
We introduce RELTA-SGLD, a taming scheme that stabilizes superlinear stochastic-gradient updates while reducing unnecessary suppression of the original learning drift. A threshold determines where the taming turns on, wh…
Deterministic Envelopes for Tamed SGLD: Decoupling Stochastic Gradient Noise and Localizing Taming
Stochastic gradient Langevin algorithms often use tamed denominators to stabilize superlinear drifts. This paper shows that when the denominator depends on the current stochastic gradient, the transformed update can have…
Adaptive Non-reversible Stochastic Gradient Langevin Dynamics
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 adap…
Adaptively Preconditioned Stochastic Gradient Langevin Dynamics
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 adap…
Navigate