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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…

Machine Learning · Statistics 2020-12-22 Pranay Sharma , Kaidi Xu , Sijia Liu , Pin-Yu Chen , Xue Lin , Pramod K. Varshney

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…

Machine Learning · Computer Science 2025-10-24 Shaocong Ma , Heng Huang

Iterative optimization is central to modern artificial intelligence (AI) and provides a crucial framework for understanding adaptive systems. This review provides a unified perspective on this subject, bridging classic theory with neural…

Machine Learning · Computer Science 2025-10-22 Jesús García Fernández , Nasir Ahmad , Marcel van Gerven

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.…

Machine Learning · Computer Science 2024-10-10 Elissa Mhanna , Mohamad Assaad

Zeroth-order or derivative-free optimization (MeZO) is an attractive strategy for finetuning large language models (LLMs) because it eliminates the memory overhead of backpropagation. However, it converges slowly due to the inherent curse…

Machine Learning · Computer Science 2026-04-21 Lejs Deen Behric , Liang Zhang , Bingcong Li , Kiran Koshy Thekumparampil

Zeroth-order (ZO) optimization is being recognized as a simple yet powerful alternative to standard backpropagation (BP)-based training. Notably, ZO optimization allows for training with only forward passes and (almost) the same memory as…

Machine Learning · Computer Science 2025-01-09 Keisuke Sugiura , Hiroki Matsutani

Zeroth-order (ZO) fine-tuning is attractive for large language models because it replaces backpropagation with forward objective evaluations. Existing implementations nevertheless execute ZO algorithms inside conventional training loops,…

Machine Learning · Computer Science 2026-05-28 Zelin Li , Caiwen Ding

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…

Machine Learning · Computer Science 2020-05-20 Daniel Golovin , John Karro , Greg Kochanski , Chansoo Lee , Xingyou Song , Qiuyi Zhang

Zeroth-order methods are extensively used in machine learning applications where gradients are infeasible or expensive to compute, such as black-box attacks, reinforcement learning, and language model fine-tuning. Existing optimization…

Machine Learning · Computer Science 2025-11-12 Liang Zhang , Bingcong Li , Kiran Koshy Thekumparampil , Sewoong Oh , Michael Muehlebach , Niao He

We study the problem of training neural networks with quantized parameters. Learning low-precision quantized parameters by enabling computation of gradients via the Straight-Through Estimator (STE) can be challenging. While the STE enables…

Machine Learning · Computer Science 2025-10-29 Ningfeng Yang , Tor M. Aamodt

This paper introduces a class of model-free feedback methods for solving generic constrained optimization problems where the specific mathematical forms of the objective and constraint functions are not available. The proposed methods,…

Optimization and Control · Mathematics 2025-02-13 Xin Chen , Jorge I. Poveda , Na Li

Zeroth-order (ZO) method has been shown to be a powerful method for solving the optimization problem where explicit expression of the gradients is difficult or infeasible to obtain. Recently, due to the practical value of the constrained…

Optimization and Control · Mathematics 2024-09-04 Wanli Shi , Hongchang Gao , Bin Gu

A major challenge of applying zeroth-order (ZO) methods is the high query complexity, especially when queries are costly. We propose a novel gradient estimation technique for ZO methods based on adaptive lazy queries that we term as LAZO.…

Machine Learning · Computer Science 2022-06-16 Quan Xiao , Qing Ling , Tianyi Chen

Large Vision-Language Models (VLMs) enable strong multimodal reasoning but incur heavy inference costs from redundant visual tokens. Token pruning alleviates this issue, yet existing approaches face limitations. Attention-based methods rely…

Computer Vision and Pattern Recognition · Computer Science 2026-03-23 Youngeun Kim , Youjia Zhang , Huiling Liu , Aecheon Jung , Sunwoo Lee , Sungeun Hong

Recently, zeroth-order (ZO) optimization plays an essential role in scenarios where gradient information is inaccessible or unaffordable, such as black-box systems and resource-constrained environments. While existing adaptive methods such…

Machine Learning · Computer Science 2025-06-10 Yao Shu , Qixin Zhang , Kun He , Zhongxiang Dai

In this letter, we first propose a \underline{Z}eroth-\underline{O}rder c\underline{O}ordinate \underline{M}ethod~(ZOOM) to solve the stochastic optimization problem over a decentralized network with only zeroth-order~(ZO) oracle feedback…

Optimization and Control · Mathematics 2022-10-11 Shengjun Zhang , Tan Shen , Hongwei Sun , Yunlong Dong , Dong Xie , Heng Zhang

$\ell_0$ 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…

Machine Learning · Computer Science 2024-03-19 William de Vazelhes , Hualin Zhang , Huimin Wu , Xiao-Tong Yuan , Bin Gu

Zeroth-order (ZO) optimization provides a powerful framework for problems where explicit gradients are unavailable and have to be approximated using only queries to function value. The prevalent single-query approach is simple, but suffers…

Machine Learning · Computer Science 2026-02-03 Wei Lin , Qingyu Song , Hong Xu

Orthogonality-based optimizers, such as Muon, have recently shown strong performance across large-scale training and community-driven efficiency challenges. However, these methods rely on a costly gradient orthogonalization step. Even…

Artificial Intelligence · Computer Science 2025-12-05 Thibaut Boissin , Thomas Massena , Franck Mamalet , Mathieu Serrurier

Zeroth-order (ZO) optimization with ordinal feedback has emerged as a fundamental problem in modern machine learning systems, particularly in human-in-the-loop settings such as reinforcement learning from human feedback, preference…

Optimization and Control · Mathematics 2025-12-23 Haishan Ye