Optimal Extragradient-Based Stochastic Bilinearly-Coupled Saddle-Point Optimization

We consider the smooth convex-concave bilinearly-coupled saddle-point problem, $\min_{\mathbf{x}}\max_{\mathbf{y}}~F(\mathbf{x}) + H(\mathbf{x},\mathbf{y}) – G(\mathbf{y})$, where one has access to stochastic first-order oracles for $F$, $G$ as well as the bilinear coupling function $H$. Building upon standard stochastic extragradient analysis for variational inequalities, we present a stochastic \emph{accelerated gradient-extragradient (AG-EG)} descent-ascent algorithm that combines extragradient and Nesterov’s … Read more

Understanding the Acceleration Phenomenon via High-Resolution Differential Equations

Gradient-based optimization algorithms can be studied from the perspective of limiting or- dinary differential equations (ODEs). Motivated by the fact that existing ODEs do not distin- guish between two fundamentally different algorithms—Nesterov’s accelerated gradient method for strongly convex functions (NAG-SC) and Polyak’s heavy-ball method—we study an alter- native limiting process that yields high-resolution ODEs. We … Read more