The differential equation (DE) approach for convex optimization, which relates optimization
methods to specific continuous DEs with rate-revealing Lyapunov functionals, has gained …

Existing analyses of optimization in deep learning are either continuous, focusing on
(variants of) gradient flow, or discrete, directly treating (variants of) gradient descent …

We analyze continuous-time models of accelerated gradient methods through deriving
conservation laws in dilated coordinate systems. Namely, instead of analyzing the dynamics …

Remarkable prevalence of cloud computing has enabled smart cars to provide infotainment
services. However, retrieving infotainment contents from long-distance data centers poses a …

In this paper, we investigate a Lyapunov-like differential inequality that allows us to establish
finite-time stability of a continuous-time state-space dynamical system represented via a …

This work proposes an accelerated primal-dual dynamical system for affine constrained
convex optimization and presents a class of primal-dual methods with nonergodic …

Recently, continuous-time dynamical systems have proved useful in providing conceptual
and quantitative insights into gradient-based optimization, widely used in modern machine …

Motivated by applications in reinforcement learning (RL), we study a nonlinear stochastic
approximation (SA) algorithm under Markovian noise, and establish its finite-sample …

We propose a novel data-driven method to accelerate the convergence of Alternating
Direction Method of Multipliers (ADMM) for solving distributed DC optimal power flow (DC …

Arguably, the two most popular accelerated or momentum-based optimization methods are
Nesterov's accelerated gradient and Polyaks's heavy ball, both corresponding to different …