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As application demands for zeroth-order (gradient-free) optimization accelerate, the need for variance reduced and faster converging approaches is also intensifying. This paper addresses these challenges by presenting: a) a comprehensive…

Machine Learning · Computer Science 2018-06-08 Sijia Liu , Bhavya Kailkhura , Pin-Yu Chen , Paishun Ting , Shiyu Chang , Lisa Amini

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…

Optimization and Control · Mathematics 2024-10-04 Bin Gu , Xiyuan Wei , Hualin Zhang , Yi Chang , Heng Huang

Fine-tuning language models (LMs) has demonstrated success in a wide array of downstream tasks. However, as LMs are scaled up, the memory requirements for backpropagation become prohibitively high. Zeroth-order (ZO) optimization methods can…

Machine Learning · Computer Science 2024-04-15 Tanmay Gautam , Youngsuk Park , Hao Zhou , Parameswaran Raman , Wooseok Ha

Variance reduction techniques are designed to decrease the sampling variance, thereby accelerating convergence rates of first-order (FO) and zeroth-order (ZO) optimization methods. However, in composite optimization problems, ZO methods…

Machine Learning · Computer Science 2024-05-29 Hao Di , Haishan Ye , Yueling Zhang , Xiangyu Chang , Guang Dai , Ivor W. Tsang

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…

Optimization and Control · Mathematics 2026-03-03 Ruiyang Jin , Yuke Zhou , Yujie Tang , Jie Song , Siyang Gao

Stochastic First-Order (SFO) methods have been a cornerstone in addressing a broad spectrum of modern machine learning (ML) challenges. However, their efficacy is increasingly questioned, especially in large-scale applications where…

Machine Learning · Computer Science 2024-08-01 Di Zhang , Suvrajeet Sen

In the evolving landscape of natural language processing (NLP), fine-tuning pre-trained Large Language Models (LLMs) with first-order (FO) optimizers like SGD and Adam has become standard. Yet, as LLMs grow {in size}, the substantial memory…

Zeroth-order (ZO) optimization provides a gradient-free alternative to first-order (FO) methods by estimating gradients via finite differences of function evaluations, and has recently emerged as a memory-efficient paradigm for fine-tuning…

Machine Learning · Computer Science 2026-02-24 Yicheng Lang , Changsheng Wang , Yihua Zhang , Mingyi Hong , Zheng Zhang , Wotao Yin , Sijia Liu

Fine-tuning large language models (LLMs) often faces GPU memory bottlenecks: the backward pass of first-order optimizers like Adam increases memory usage to more than 10 times the inference level (e.g., 633 GB for OPT-30B). Zeroth-order…

Machine Learning · Computer Science 2025-07-01 Sizhe Dang , Yangyang Guo , Yanjun Zhao , Haishan Ye , Xiaodong Zheng , Guang Dai , Ivor Tsang

Proximal gradient method has been playing an important role to solve many machine learning tasks, especially for the nonsmooth problems. However, in some machine learning problems such as the bandit model and the black-box learning problem,…

Optimization and Control · Mathematics 2019-02-19 Feihu Huang , Bin Gu , Zhouyuan Huo , Songcan Chen , Heng Huang

Fine-tuning large language models (LLMs) has achieved remarkable success across various NLP tasks, but the substantial memory overhead during backpropagation remains a critical bottleneck, especially as model scales grow. Zeroth-order (ZO)…

Computation and Language · Computer Science 2026-01-09 Feihu Jin , Shipeng Cen , Ying Tan

Fine-tuning is powerful for adapting large language models to downstream tasks, but it often results in huge memory usages. A promising approach to mitigate this is using Zeroth-Order (ZO) optimization, which estimates gradients to replace…

Machine Learning · Computer Science 2024-10-15 Fei Wang , Li Shen , Liang Ding , Chao Xue , Ye Liu , Changxing Ding

First-order methods for stochastic optimization have undeniable relevance, in part due to their pivotal role in machine learning. Variance reduction for these algorithms has become an important research topic. In contrast to common…

Machine Learning · Computer Science 2021-09-08 Manuel Madeira , Renato Negrinho , João Xavier , Pedro M. Q. Aguiar

Fine-tuning Large Language Models (LLMs) is essential for adapting pre-trained models to downstream tasks. Yet traditional first-order optimizers such as Stochastic Gradient Descent (SGD) and Adam incur prohibitive memory and computational…

Fine-tuning large language models (LLMs) using standard first-order (FO) optimization often drives training toward sharp, poorly generalizing minima. Conversely, zeroth-order (ZO) methods offer stronger exploratory behavior without relying…

Machine Learning · Computer Science 2026-01-12 Feihu Jin , Ying Tan

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

This paper investigates zeroth-order (ZO) finite-sum composite optimization. Recently, variance reduction techniques have been applied to ZO methods to mitigate the non-vanishing variance of 2-point estimators in constrained/composite…

Optimization and Control · Mathematics 2026-01-09 Silan Zhang , Yujie Tang

Large language models (LLMs) excel across various tasks, but standard first-order (FO) fine-tuning demands considerable memory, significantly limiting real-world deployment. Recently, zeroth-order (ZO) optimization stood out as a promising…

Machine Learning · Computer Science 2025-11-04 Qitao Tan , Jun Liu , Zheng Zhan , Caiwei Ding , Yanzhi Wang , Xiaolong Ma , Jaewoo Lee , Jin Lu , Geng Yuan

Many important machine learning applications amount to solving minimax optimization problems, and in many cases there is no access to the gradient information, but only the function values. In this paper, we focus on such a gradient-free…

Machine Learning · Computer Science 2021-03-23 Tengyu Xu , Zhe Wang , Yingbin Liang , H. Vincent Poor

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…

Machine Learning · Computer Science 2019-10-29 Kaiyi Ji , Zhe Wang , Yi Zhou , Yingbin Liang
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