langevindynamic
Stochastic Gradient Hamiltonian Monte Carlo Methods with Recursive Variance Reduction
Difan Zou, Pan Xu, Quanquan Gu
Figure 3: Ex represents (c)-(d) ConB.
Global Convergence of Langevin Dynamics Based Algorithms for Nonconvex Optimization
Pan Xu, Jinghui Chen, Difan Zou, Quanquan Gu
Let x = argminx2RdFn(x) betheglobalminimizerofFn.
Efficiently escaping saddle points on manifolds
Christopher Criscitiello, Nicolas Boumal
Ifthext, krf(xt)k , perturbxt by , with sampled zero.
Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices
Santosh Vempala, Andre Wibisono
See Theorem 2 in Section 3.1 formoredetail.
Generative Modeling by Estimating Gradients of the Data Distribution
Generative models have many applications in machine learning. To list a few, they have been usedtogenerate high-fidelity images [26,6],synthesize realistic speech andmusic fragments [58], improve the performance of semi-supervised learning [28, 10], detect adversarial examples and other anomalous data [54], imitation learning [22], and explore promising states in reinforcement learning [41].
50cf0fe63e0ff857e1c9d01d827267ca-Paper.pdf
In this work, we establish rapid convergence for these algorithms under distance measures more suitable for differential privacy.
Mirror Langevin Monte Carlo: the Case Under Isoperimetry
Four Newton Lange /exp( ), taking (x)= log x21) l asthebarrier = 4 so Stepsizeish= 10 5. Projected constraints, directly byprojection andtheproximal solvedwith suggesting