This paper resolves a longstanding open question pertaining to the design of near-optimal
first-order algorithms for smooth and strongly-convex-strongly-concave minimax problems …

Despite its important applications in Machine Learning, min-max optimization of objective
functions that are nonconvex-nonconcave remains elusive. Not only are there no known first …

This paper studies first order methods for solving smooth minimax optimization problems
$\min_x\max_y g (x, y) $ where $ g (\cdot,\cdot) $ is smooth and $ g (x,\cdot) $ is concave for …

In this work, we study the computational complexity of reducing the squared gradient
magnitude for smooth minimax optimization problems. First, we present algorithms with …

During the recent years the interest of optimization and machine learning communities in
high-probability convergence of stochastic optimization methods has been growing. One of …

Modern minimax problems, such as generative adversarial network and adversarial training,
are often under a nonconvex-nonconcave setting, and develo** an efficient method for …

We study the question of obtaining last-iterate convergence rates for no-regret learning
algorithms in multi-player games. We show that the optimistic gradient (OG) algorithm with a …

Motivated by applications in Game Theory, Optimization, and Generative Adversarial
Networks, recent work of Daskalakis et al\cite {DISZ17} and follow-up work of Liang and …

In this paper, we consider nonconvex minimax optimization, which is gaining prominence in
many modern machine learning applications, such as GANs. Large-scale edge-based …

In this paper, we study the lower iteration complexity bounds for finding the saddle point of a
strongly convex and strongly concave saddle point problem: min x max y F (x, y). We restrict …