Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Nonconvex Stochastic Optimization: Nonasymptotic Performance Bounds and Momentum-Based Acceleration

On sampling from a log-concave density using kinetic Langevin diffusions

(2020) Arnak S. Dalalyan et al.   BERNOULLI

User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient

(2019) Arnak S. Dalalyan et al.   STOCHASTIC PROCESSES AND THEIR APPLICATIONS

Couplings and quantitative contraction rates for Langevin dynamics

(2019) Andreas Eberle et al.   ANNALS OF PROBABILITY

On variance reduction for stochastic smooth convex optimization with multiplicative noise

(2018) Alejandro Jofré et al.   MATHEMATICAL PROGRAMMING

Accelerated Methods for NonConvex Optimization

(2018) Yair Carmon et al.   SIAM JOURNAL ON OPTIMIZATION

The landscape of empirical risk for nonconvex losses

(2018) Song Mei et al.   ANNALS OF STATISTICS

Behavior of accelerated gradient methods near critical points of nonconvex functions

(2018) Michael O’Neill et al.   MATHEMATICAL PROGRAMMING

Complete Dictionary Recovery Over the Sphere I: Overview and the Geometric Picture

(2017) Ju Sun et al.   IEEE TRANSACTIONS ON INFORMATION THEORY

Theoretical guarantees for approximate sampling from smooth and log-concave densities

(2016) Arnak S. Dalalyan   JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY

Accelerated gradient methods for nonconvex nonlinear and stochastic programming

(2015) Saeed Ghadimi et al.   MATHEMATICAL PROGRAMMING

Robust Variable Selection With Exponential Squared Loss

(2013) Xueqin Wang et al.   JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION