We propose stochastic variance reduced algorithms for solving convex-concave saddle
point problems, monotone variational inequalities, and monotone inclusions. Our framework …

Many tasks in modern machine learning can be formulated as finding equilibria in\emph
{sequential} games. In particular, two-player zero-sum sequential games, also known as …

Training generative adversarial networks requires balancing of delicate adversarial
dynamics. Even with careful tuning, training may diverge or end up in a bad equilibrium with …

We introduce a new algorithm for the numerical computation of Nash equilibria of
competitive two-player games. Our method is a natural generalization of gradient descent to …

A growing number of learning methods are actually differentiable games whose players
optimise multiple, interdependent objectives in parallel--from GANs and intrinsic curiosity to …

Deep learning is built on the foundational guarantee that gradient descent on an objective
function converges to local minima. Unfortunately, this guarantee fails in settings, such as …

Neural networks can be trained to solve partial differential equations (PDEs) by using the
PDE residual as the loss function. This strategy is called" physics-informed neural …

Generative adversarial networks (GANs) are known to achieve the state-of-the-art
performance on various generative tasks, but these results come at the expense of a …

Abstract The instability of Generative Adversarial Network (GAN) training has frequently
been attributed to gradient descent. Consequently, recent methods have aimed to tailor the …

We consider a general-sum N-player linear-quadratic game with stochastic dynamics over a
finite horizon and prove the global convergence of the natural policy gradient method to the …