Related papers: GANs May Have No Nash Equilibria

We study a distributionally robust optimization formulation (i.e., a min-max game) for two representative problems in Bayesian nonparametric estimation: Gaussian process regression and, more generally, linear inverse problems. Our…

We introduce a novel framework for adversarial training where the target distribution is annealed between the uniform distribution and the data distribution. We posited a conjecture that learning under continuous annealing in the…

Robust utility optimization enables an investor to deal with market uncertainty in a structured way, with the goal of maximizing the worst-case outcome. In this work, we propose a generative adversarial network (GAN) approach to…

Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…

Graphical games are a useful framework for modeling the interactions of (selfish) agents who are connected via an underlying topology and whose behaviors influence each other. They have wide applications ranging from computer science to…

Generative adversarial networks (GANs) represent a powerful tool for classical machine learning: a generator tries to create statistics for data that mimics those of a true data set, while a discriminator tries to discriminate between the…

Adversarial formulations such as generative adversarial networks (GANs) have rekindled interest in two-player min-max games. A central obstacle in the optimization of such games is the rotational dynamics that hinder their convergence. In…

This paper establishes the tractability of finding the optimal Nash equilibrium, as well as the optimal social solution, to a discrete congestion game using a gate-model quantum computer. The game is of the type originally posited by…

We prove the existence of Bayesian Nash Equilibrium (BNE) of general-sum Bayesian games with continuous types and finite actions under the conditions that the utility functions and the prior type distributions are continuous concerning the…

Wasserstein GANs are based on the idea of minimising the Wasserstein distance between a real and a generated distribution. We provide an in-depth mathematical analysis of differences between the theoretical setup and the reality of training…

Motivated by the pursuit of a systematic computational and algorithmic understanding of Generative Adversarial Networks (GANs), we present a simple yet unified non-asymptotic local convergence theory for smooth two-player games, which…

We propose a type of non-cooperative game, termed multi-cluster aggregative game, which is composed of clusters as players, where each cluster consists of collaborative agents with cost functions depending on their own decisions and the…

We consider sequences of games $\mathcal{G}=\{G_1,G_2,\ldots\}$ where, for all $n$, $G_n$ has the same set of players. Such sequences arise in the analysis of running time of players in games, in electronic money systems such as Bitcoin and…

Generative adversarial networks (GANs) can be interpreted as an adversarial game between two players, a discriminator D and a generator G, in which D learns to classify real from fake data and G learns to generate realistic data by…

Generative adversarial networks (GANs) have received a tremendous amount of attention in the past few years, and have inspired applications addressing a wide range of problems. Despite its great potential, GANs are difficult to train.…

This paper investigates a class of linear-quadratic-Gaussian risk-sensitive graphon mean-field games, involving an asymptotically infinite population of heterogeneous agents distributed across an asymptotically infinite network, where each…

Despite being impactful on a variety of problems and applications, the generative adversarial nets (GANs) are remarkably difficult to train. This issue is formally analyzed by \cite{arjovsky2017towards}, who also propose an alternative…

Generative Adversarial Networks (GANs) have become a powerful framework to learn generative models that arise across a wide variety of domains. While there has been a recent surge in the development of numerous GAN architectures with…

The standard risk minimization paradigm of machine learning is brittle when operating in environments whose test distributions are different from the training distribution due to spurious correlations. Training on data from many…

Zero-shot learning (ZSL) aims to recognize the novel classes which cannot be collected for training a prediction model. Accordingly, generative models (e.g., generative adversarial network (GAN)) are typically used to synthesize the visual…