1 citations · 1 across the 8 of their papers we have counts for
9 papers
Online Covariance Estimation for Averaged Stochastic Gradient Descent on Riemannian Manifolds
Jingrong Guan, Liwei Jiang, Sen Na
We study online inference for averaged Riemannian stochastic gradient descent (RSGD) when the unknown parameter lies on a manifold. Although the averaged RSGD iterate is asymptotic…
Optimal Parameter-Free First-Order Methods for Convex Optimization with Unknown Growth and Smoothness
Liwei Jiang, Ke Tang, Zhe Zhang
We study deterministic first-order minimization of a convex function without prior knowledge of the objective's growth, smoothness regime, or associated parameters. We develop anyt…
Instance-optimal stochastic convex optimization: Can we improve upon sample-average and robust stochastic approximation?
Liwei Jiang, Ashwin Pananjady
We study the unconstrained minimization of a smooth and strongly convex population loss function under a stochastic oracle that introduces both additive and multiplicative noise; t…
Preconditioned subgradient method for composite optimization: overparameterization and fast convergence
Mateo Díaz, Liwei Jiang, Abdel Ghani Labassi
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing appl…
Online Covariance Estimation in Nonsmooth Stochastic Approximation
Liwei Jiang, Abhishek Roy, Krishna Balasubramanian +3
We consider applying stochastic approximation (SA) methods to solve nonsmooth variational inclusion problems. Existing studies have shown that the averaged iterates of SA methods e…
Gradient descent with adaptive stepsize converges (nearly) linearly under fourth-order growth
Damek Davis, Dmitriy Drusvyatskiy, Liwei Jiang
A prevalent belief among optimization specialists is that linear convergence of gradient descent is contingent on the function growing quadratically away from its minimizers. In th…
Asymptotic normality and optimality in nonsmooth stochastic approximation
Damek Davis, Dmitriy Drusvyatskiy, Liwei Jiang
In their seminal work, Polyak and Juditsky showed that stochastic approximation algorithms for solving smooth equations enjoy a central limit theorem. Moreover, it has since been a…
A nearly linearly convergent first-order method for nonsmooth functions with quadratic growth
Damek Davis, Liwei Jiang
Classical results show that gradient descent converges linearly to minimizers of smooth strongly convex functions. A natural question is whether there exists a locally nearly linea…
Active manifolds, stratifications, and convergence to local minima in nonsmooth optimization
Damek Davis, Dmitriy Drusvyatskiy, Liwei Jiang
We show that the subgradient method converges only to local minimizers when applied to generic Lipschitz continuous and subdifferentially regular functions that are definable in an…