相关论文: Gentlest ascent dynamics on manifolds defined by a…

We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such…

Gradient descent-ascent (GDA) flows play a central role in finding saddle points of bivariate functionals, with applications in optimization, game theory, and robust control. While they are well-understood in Hilbert and Banach spaces via…

Nonconvex optimization underlies many modern machine learning and control tasks, where saddle points pose the dominant obstacle to reliable convergence in high-dimensional settings. Escaping these saddle points deterministically using…

Generative Adversarial Networks (GAN) can achieve promising performance on learning complex data distributions on different types of data. In this paper, we first show a straightforward extension of existing GAN algorithm is not applicable…

Nonconvex-concave min-max problem arises in many machine learning applications including minimizing a pointwise maximum of a set of nonconvex functions and robust adversarial training of neural networks. A popular approach to solve this…

In this paper, we give a sharp analysis for Stochastic Gradient Descent (SGD) and prove that SGD is able to efficiently escape from saddle points and find an $(\epsilon, O(\epsilon^{0.5}))$-approximate second-order stationary point in…

Motivated by the super-diffusivity of self-repelling random walk, which has roots in statistical physics, this paper develops a new perturbation mechanism for optimization algorithms. In this mechanism, perturbations are adapted to the…

Min-max saddle point games have recently been intensely studied, due to their wide range of applications, including training Generative Adversarial Networks (GANs). However, most of the recent efforts for solving them are limited to special…

Stochastic gradient descent (SGD) is a powerful optimization technique that is particularly useful in online learning scenarios. Its convergence analysis is relatively well understood under the assumption that the data samples are…

Stochastic gradient descent (SGD) with stochastic momentum is popular in nonconvex stochastic optimization and particularly for the training of deep neural networks. In standard SGD, parameters are updated by improving along the path of the…

This work presents a numerical analysis of computing transition states of semilinear elliptic partial differential equations (PDEs) via the index-1 saddle dynamics, or equivalently, the gentlest ascent dynamics. To establish clear…

Adaptive densification is the engine of 3D Gaussian Splatting (3DGS). However, when transposed to the optimization-based Generative Distillation paradigm, this reconstruction-native mechanism reveals fundamental limitations, resulting in…

We consider the problem of convergence to a saddle point of a concave-convex function via gradient dynamics. Since first introduced by Arrow, Hurwicz and Uzawa in [1] such dynamics have been extensively used in diverse areas, there are,…

Stochastic Gradient Descent (SGD) with adaptive steps is widely used to train deep neural networks and generative models. Most theoretical results assume that it is possible to obtain unbiased gradient estimators, which is not the case in…

In recent years, there has been considerable interest in designing stochastic first-order algorithms to tackle finite-sum smooth minimax problems. To obtain the gradient estimates, one typically relies on the uniform…

Following the introduction of Adam, several novel adaptive optimizers for deep learning have been proposed. These optimizers typically excel in some tasks but may not outperform Adam uniformly across all tasks. In this work, we introduce…

This paper proposes an adaptive dynamic programming-based adaptive-gain sliding mode control (ADP-ASMC) scheme for a fixed-wing unmanned aerial vehicle (UAV) with matched and unmatched disturbances. Starting from the dynamic of fixed-wing…

Model reduction is a key technology for large-scale physical systems in science and engineering, as it brings behavior expressed in many degrees of freedom to a more manageable size that subsequently allows control, optimization, and…

Gradient descent (GD) and stochastic gradient descent (SGD) are the workhorses of large-scale machine learning. While classical theory focused on analyzing the performance of these methods in convex optimization problems, the most notable…

We introduce a novel and efficient algorithm called the stochastic approximate gradient descent (SAGD), as an alternative to the stochastic gradient descent for cases where unbiased stochastic gradients cannot be trivially obtained.…