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 …

The cornerstone underpinning deep learning is the guarantee that gradient descent on an
objective converges to local minima. Unfortunately, this guarantee fails in settings, such as …

Games generalize the single-objective optimization paradigm by introducing different
objective functions for different players. Differentiable games often proceed by simultaneous …

In optimization, the negative gradient of a function denotes the direction of steepest descent.
Furthermore, traveling in any direction orthogonal to the gradient maintains the value of the …

The success of adversarial formulations in machine learning has brought renewed
motivation for smooth games. In this work, we focus on the class of stochastic Hamiltonian …

Games are an increasingly useful tool for training and testing learning algorithms. Recent
examples include GANs, AlphaZero and the AlphaStar league. However, multi-agent …

Differentiable programming techniques are widely used in the community and are
responsible for the machine learning renaissance of the past several decades. While these …

Contemporary work on learning in continuous games has commonly overlooked the
hierarchical decision-making structure present in machine learning problems formulated as …

This paper investigates the convergence of learning dynamics in Stackelberg games. In the
class of games we consider, there is a hierarchical game being played between a leader …

Motivated by the pursuit of a systematic computational and algorithmic understanding of
Generative Adversarial Networks (GANs), we present a simple yet unified non-asymptotic …