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The two key players in Generative Adversarial Networks (GANs), the discriminator and generator, are usually parameterized as deep neural networks (DNNs). On many generative tasks, GANs achieve state-of-the-art performance but are often…
Offline multi-agent reinforcement learning in general-sum settings is challenged by the distribution shift between logged datasets and target equilibrium policies. While standard methods rely on manual pessimistic penalties, we demonstrate…
The standard approach for dealing with the ill-posedness of the training problem in machine learning and/or the reconstruction of a signal from a limited number of measurements is regularization. The method is applicable whenever the…
Generative adversarial networks (GANs) are designed with the help of min-max optimization problems that are solved with stochastic gradient-type algorithms which are known to be non-robust. In this work we revisit a non-adversarial method…
One of the challenges in the study of Generative Adversarial Networks (GANs) is the difficulty of its performance control. Lipschitz constraint is essential in guaranteeing training stability for GANs. Although heuristic methods such as…
Generative Adversarial Networks (GANs) have been shown to be powerful and flexible priors when solving inverse problems. One challenge of using them is overcoming representation error, the fundamental limitation of the network in…
In this paper, we present the Lipschitz regularization theory and algorithms for a novel Loss-Sensitive Generative Adversarial Network (LS-GAN). Specifically, it trains a loss function to distinguish between real and fake samples by…
Generative Adversarial Networks are a popular method for learning distributions from data by modeling the target distribution as a function of a known distribution. The function, often referred to as the generator, is optimized to minimize…
We present a general computational framework for solving continuous-time financial market equilibria under minimal modeling assumptions while incorporating realistic financial frictions, such as trading costs, and supporting multiple…
While deep learning in the form of recurrent neural networks (RNNs) has caused a significant improvement in neural language modeling, the fact that they are extremely prone to overfitting is still a mainly unresolved issue. In this paper we…
Natural images can be regarded as residing in a manifold that is embedded in a higher dimensional Euclidean space. Generative Adversarial Networks (GANs) try to learn the distribution of the real images in the manifold to generate samples…
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…
Modern generative adversarial networks (GANs) predominantly use piecewise linear activation functions in discriminators (or critics), including ReLU and LeakyReLU. Such models learn piecewise linear mappings, where each piece handles a…
Regularization, whether explicit in terms of a penalty in the loss or implicit in the choice of algorithm, is a cornerstone of modern machine learning. Indeed, controlling the complexity of the model class is particularly important when…
Generative Adversarial Networks (GANs) are one of the most practical methods for learning data distributions. A popular GAN formulation is based on the use of Wasserstein distance as a metric between probability distributions.…
Despite success on a wide range of problems related to vision, generative adversarial networks (GANs) often suffer from inferior performance due to unstable training, especially for text generation. To solve this issue, we propose a new…
We consider the nonstationary iterated Tikhonov regularization in Banach spaces which defines the iterates via minimization problems with uniformly convex penalty term. The penalty term is allowed to be non-smooth to include $L^1$ and total…
Generative Adversarial Networks (GANs) are popular and successful generative models. Despite their success, optimization is notoriously challenging. In this work, we explain the success and limitations of GANs by casting them as Bayesian…
The Generative Models have gained considerable attention in the field of unsupervised learning via a new and practical framework called Generative Adversarial Networks (GAN) due to its outstanding data generation capability. Many models of…
A generative adversarial network (GAN) has been a representative backbone model in generative artificial intelligence (AI) because of its powerful performance in capturing intricate data-generating processes. However, the GAN training is…