相关论文: MGDA Converges under Generalized Smoothness, Prova…

Optimization of conflicting functions is of paramount importance in decision making, and real world applications frequently involve data that is uncertain or unknown, resulting in multi-objective optimization (MOO) problems of stochastic…

Recent studies have shown that many nonconvex machine learning problems satisfy a generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms are not fully adapted to such…

This paper is devoted to the study of stochastic optimization problems under the generalized smoothness assumption. By considering the unbiased gradient oracle in Stochastic Gradient Descent, we provide strategies to achieve in bounds the…

$L_0$-smoothness, which has been pivotal to advancing decentralized optimization theory, is often fairly restrictive for modern tasks like deep learning. The recent advent of relaxed $(L_0,L_1)$-smoothness condition enables improved…

Recently, there has been an increasing interest in the application of multiobjective optimization (MOO) in machine learning (ML). This interest is driven by the numerous real-life situations where multiple objectives must be optimized…

As one of the most fundamental stochastic optimization algorithms, stochastic gradient descent (SGD) has been intensively developed and extensively applied in machine learning in the past decade. There have been some modified SGD-type…

We study the iteration complexity of the optimistic gradient descent-ascent (OGDA) method and the extra-gradient (EG) method for finding a saddle point of a convex-concave unconstrained min-max problem. To do so, we first show that both…

Excessive computational cost for learning large data and streaming data can be alleviated by using stochastic algorithms, such as stochastic gradient descent and its variants. Recent advances improve stochastic algorithms on convergence…

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

The success of minimax learning problems of generative adversarial networks (GANs) has been observed to depend on the minimax optimization algorithm used for their training. This dependence is commonly attributed to the convergence speed…

Stochastic smooth nonconvex minimax problems are prevalent in machine learning, e.g., GAN training, fair classification, and distributionally robust learning. Stochastic gradient descent ascent (GDA)-type methods are popular in practice due…

This paper formalizes and analyzes Gaussian smoothing applied to two prominent optimization methods: Stochastic Gradient Descent (GSmoothSGD) and Adam (GSmoothAdam) in deep learning. By attenuating small fluctuations, Gaussian smoothing…

The classical convergence analysis of SGD is carried out under the assumption that the norm of the stochastic gradient is uniformly bounded. While this might hold for some loss functions, it is violated for cases where the objective…

Recently, multi-objective optimization (MOO) has gained attention for its broad applications in ML, operations research, and engineering. However, MOO algorithm design remains in its infancy and many existing MOO methods suffer from…

In recent years, a variety of gradient-based methods have been developed to solve Bi-Level Optimization (BLO) problems in machine learning and computer vision areas. However, the theoretical correctness and practical effectiveness of these…

We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…

Non-convex optimization problems are ubiquitous in machine learning, especially in Deep Learning. While such complex problems can often be successfully optimized in practice by using stochastic gradient descent (SGD), theoretical analysis…

The gradient descent (GD) method -- is a fundamental and likely the most popular optimization algorithm in machine learning (ML), with a history traced back to a paper in 1847 (Cauchy, 1847). It was studied under various assumptions,…

Multi-Objective Bi-Level Optimization (MOBLO) addresses nested multi-objective optimization problems common in a range of applications. However, its multi-objective and hierarchical bilevel nature makes it notably complex. Gradient-based…

The generalized smooth condition, $(L_{0},L_{1})$-smoothness, has triggered people's interest since it is more realistic in many optimization problems shown by both empirical and theoretical evidence. Two recent works established the…