Uday V. Shanbhag

Variance-Reduced Accelerated First-order Methods: Central Limit Theorems and Confidence Statements

2020 · arXiv (Cornell University)

In this paper, we study a stochastic strongly convex optimization problem and propose three classes of variable sample-size stochastic first-order methods including the standard stochastic gradient descent method, its accelerated variant, and the stochastic heavy …

Zeroth-order Gradient and Quasi-Newton Methods for Nonsmooth Nonconvex Stochastic Optimization

2023 · arXiv (Cornell University)

We consider the minimization of a Lipschitz continuous and expectation-valued function, denoted by $f$ and defined as $f(\mathbf{x}) \triangleq \mathbb{E}[\tilde{f}(\mathbf{x}, \mathbfξ)]$, over a closed and convex set $\mathcal{X}$. We obtain asymptotics as well as rate …