Related papers: Complex Momentum for Optimization in Games

Generative adversarial network (GAN) is among the most popular deep learning models for learning complex data distributions. However, training a GAN is known to be a challenging task. This is often attributed to the lack of correlation…

Since Polyak's pioneering work, heavy ball (HB) momentum has been widely studied in minimization. However, its role in min-max games remains largely unexplored. As a key component of practical min-max algorithms like Adam, this gap limits…

Adaptive gradient methods, e.g. \textsc{Adam}, have achieved tremendous success in machine learning. Scaling the learning rate element-wisely by a certain form of second moment estimate of gradients, such methods are able to attain rapid…

With the recent advances in solving large, zero-sum extensive form games, there is a growing interest in the inverse problem of inferring underlying game parameters given only access to agent actions. Although a recent work provides a…

In the recent years, various gradient descent algorithms including the methods of gradient descent, gradient descent with momentum, adaptive gradient (AdaGrad), root-mean-square propagation (RMSProp) and adaptive moment estimation (Adam)…

We investigate the resolution of second-order, potential, and monotone mean field games with the generalized conditional gradient algorithm, an extension of the Frank-Wolfe algorithm. We show that the method is equivalent to the fictitious…

Zero-sum and non-zero-sum (aka general-sum) games are relevant in a wide range of applications. While general non-zero-sum games are computationally hard, researchers focus on the special class of monotone games for gradient-based…

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 generative adversarial nets, where there are multiple…

Training deep neural networks is a challenging task. In order to speed up training and enhance the performance of deep neural networks, we rectify the vanilla conjugate gradient as conjugate-gradient-like and incorporate it into the generic…

In multi-agent settings with mixed incentives, methods developed for zero-sum games have been shown to lead to detrimental outcomes. To address this issue, opponent shaping (OS) methods explicitly learn to influence the learning dynamics of…

Gradient descent-based optimization methods underpin the parameter training of neural networks, and hence comprise a significant component in the impressive test results found in a number of applications. Introducing stochasticity is key to…

In this work, we establish a frequency-domain framework for analyzing gradient-based algorithms in linear minimax optimization problems; specifically, our approach is based on the Z-transform, a powerful tool applied in Control Theory and…

Deep learning models are known to be vulnerable to adversarial examples crafted by adding human-imperceptible perturbations on benign images. Many existing adversarial attack methods have achieved great white-box attack performance, but…

We present a manifestly covariant formulation of the gradient descent method, ensuring consistency across arbitrary coordinate systems and general curved trainable spaces. The optimization dynamics is defined using a covariant force vector…

We introduce $\mathbf{G}$radient Descent with $\mathbf{A}$daptive $\mathbf{M}$omentum $\mathbf{S}$caling ($\mathbf{Grams}$), a novel optimization algorithm that decouples the direction and magnitude of parameter updates in deep learning.…

Recent literature has demonstrated promising results for training Generative Adversarial Networks by employing a set of discriminators, in contrast to the traditional game involving one generator against a single adversary. Such methods…

The wide applications of Generative adversarial networks benefit from the successful training methods, guaranteeing that an object function converges to the local minima. Nevertheless, designing an efficient and competitive training method…

Momentum methods for convex optimization often rely on precise choices of algorithmic parameters, based on knowledge of problem parameters, in order to achieve fast convergence, as well as to prevent oscillations that could severely…

We present a new accelerated gradient-based method for solving smooth unconstrained optimization problems. The goal is to embed a heavy-ball type of momentum into the Fast Gradient Method (FGM). For this purpose, we devise a generalization…

Decentralized training of deep learning models is a key element for enabling data privacy and on-device learning over networks. In realistic learning scenarios, the presence of heterogeneity across different clients' local datasets poses an…