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Zeroth-order (ZO) optimization has emerged as a promising alternative to gradient-based backpropagation methods, particularly for black-box optimization and large language model (LLM) fine-tuning. However, ZO methods often suffer from slow…

Zeroth-order optimization (ZO) has been a powerful framework for solving black-box problems, which estimates gradients using zeroth-order data to update variables iteratively. The practical applicability of ZO critically depends on the…

Zeroth-order (ZO) optimization is one key technique for machine learning problems where gradient calculation is expensive or impossible. Several variance reduced ZO proximal algorithms have been proposed to speed up ZO optimization for…

Coordinate descent algorithms are widely used in machine learning and large-scale data analysis due to their strong optimality guarantees and impressive empirical performance in solving non-convex problems. In this work, we introduce Block…

Novel coordinate descent (CD) methods are proposed for minimizing nonconvex functions consisting of three terms: (i) a continuously differentiable term, (ii) a simple convex term, and (iii) a concave and continuous term. First, by extending…

Zeroth-order optimization is the process of minimizing an objective $f(x)$, given oracle access to evaluations at adaptively chosen inputs $x$. In this paper, we present two simple yet powerful GradientLess Descent (GLD) algorithms that do…

In this work, we focus on the study of stochastic zeroth-order (ZO) optimization which does not require first-order gradient information and uses only function evaluations. The problem of ZO optimization has emerged in many recent machine…

Nonsmooth composite optimization with orthogonality constraints has a wide range of applications in statistical learning and data science. However, this problem is challenging due to its nonsmooth objective and computationally expensive…

In this paper, we study zeroth-order algorithms for minimax optimization problems that are nonconvex in one variable and strongly-concave in the other variable. Such minimax optimization problems have attracted significant attention lately…

Two types of low cost-per-iteration gradient descent methods have been extensively studied in parallel. One is online or stochastic gradient descent (OGD/SGD), and the other is randomzied coordinate descent (RBCD). In this paper, we combine…

Two types of zeroth-order stochastic algorithms have recently been designed for nonconvex optimization respectively based on the first-order techniques SVRG and SARAH/SPIDER. This paper addresses several important issues that are still open…

Zeroth-order (ZO) optimization is popular in real-world applications that accessing the gradient information is expensive or unavailable. Recently, adaptive ZO methods that normalize gradient estimators by the empirical standard deviation…

We introduce and analyze Structured Stochastic Zeroth order Descent (S-SZD), a finite difference approach that approximates a stochastic gradient on a set of $l\leq d$ orthogonal directions, where $d$ is the dimension of the ambient space.…

$\ell_0$ constrained optimization is prevalent in machine learning, particularly for high-dimensional problems, because it is a fundamental approach to achieve sparse learning. Hard-thresholding gradient descent is a dominant technique to…

Zeroth-order optimization aims to minimize an objective function using only function evaluations, and is therefore fundamental in black-box optimization, hyperparameter tuning, bandit learning, and adversarial machine learning. While…

Zero-order (ZO) optimization is a powerful tool for dealing with realistic constraints. On the other hand, the gradient-tracking (GT) technique proved to be an efficient method for distributed optimization aiming to achieve consensus.…

Conventional learning methods simplify the bilinear model by regarding two intrinsically coupled factors independently, which degrades the optimization procedure. One reason lies in the insufficient training due to the asynchronous gradient…

We study (constrained) nonconvex (composite) optimization problems where the decision variables vector can be split into blocks of variables. Random block projection is a popular technique to handle this kind of problem for its remarkable…

We study stochastic zeroth-order (ZO) optimization of smooth nonconvex objectives under heavy-tailed sample-gradient noise. This regime is motivated by empirical evidence that gradient noise in modern machine learning can violate the…

Zeroth-order optimization (ZOO) is an important framework for stochastic optimization when gradients are unavailable or expensive to compute. A potential limitation of existing ZOO methods is the bias inherent in most gradient estimators…