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Zeroth-order (ZO) optimization has become increasingly popular and important in fine-tuning large language models (LLMs), especially on edge devices due to its ability to adjust the model to local data without the need for memory-intensive…

Machine Learning · Computer Science 2026-05-18 Jiahe Chen , Ziye Ma

Fine-tuning language models (LMs) has yielded success on diverse downstream tasks, but as LMs grow in size, backpropagation requires a prohibitively large amount of memory. Zeroth-order (ZO) methods can in principle estimate gradients using…

Machine Learning · Computer Science 2024-01-12 Sadhika Malladi , Tianyu Gao , Eshaan Nichani , Alex Damian , Jason D. Lee , Danqi Chen , Sanjeev Arora

We investigate the effectiveness of adaptive zeroth-order (ZO) optimization for memory-constrained fine-tuning of large language models (LLMs). Contrary to prior claims, we show that adaptive ZO methods such as ZO-Adam offer no convergence…

Machine Learning · Computer Science 2026-05-06 Hassan Dbouk , Nidham Gazagnadou , Matthias Reisser , Christos Louizos

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

Language Models (LLMs) are often quantized to lower precision to reduce the memory cost and latency in inference. However, quantization often degrades model performance, thus fine-tuning is required for various down-stream tasks.…

Machine Learning · Computer Science 2025-02-19 Jiajun Zhou , Yifan Yang , Kai Zhen , Ziyue Liu , Yequan Zhao , Ershad Banijamali , Athanasios Mouchtaris , Ngai Wong , Zheng Zhang

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

Fine-tuning Large Language Models (LLMs) with first-order methods like back-propagation is computationally intensive. Zeroth-Order (ZO) optimisation uses function evaluations instead of gradients, reducing memory usage, but suffers from…

Computation and Language · Computer Science 2025-07-24 Alessio Galatolo , Zhenbang Dai , Katie Winkle , Meriem Beloucif

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…

Optimization and Control · Mathematics 2026-02-03 Haishan Ye , Luo Luo

Fine-tuning vision language models (VLMs) has achieved remarkable performance across various downstream tasks; yet, it requires access to model gradients through backpropagation (BP), making them unsuitable for memory-constrained,…

Machine Learning · Computer Science 2025-10-27 Yifan Yang , Zhen Zhang , Rupak Vignesh Swaminathan , Jing Liu , Nathan Susanj , Zheng Zhang

Lowering the memory requirement in full-parameter training on large models has become a hot research area. MeZO fine-tunes the large language models (LLMs) by just forward passes in a zeroth-order SGD optimizer (ZO-SGD), demonstrating…

Machine Learning · Computer Science 2023-12-27 Shuoran Jiang , Qingcai Chen , Youchen Pan , Yang Xiang , Yukang Lin , Xiangping Wu , Chuanyi Liu , Xiaobao Song

Fine-tuning pre-trained Large Language Models (LLMs) for downstream tasks using First-Order (FO) optimizers presents significant computational challenges. Parameter-Efficient Fine-Tuning (PEFT) methods address these by freezing most model…

Machine Learning · Computer Science 2025-12-16 Reza Shirkavand , Peiran Yu , Qi He , Heng Huang

While fine-tuning large language models (LLMs) for specific tasks often yields impressive results, it comes at the cost of memory inefficiency due to back-propagation in gradient-based training. Memory-efficient Zeroth-order (MeZO)…

Machine Learning · Computer Science 2026-02-17 Yong Liu , Zirui Zhu , Chaoyu Gong , Minhao Cheng , Cho-Jui Hsieh , Yang You

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…

Machine Learning · Computer Science 2025-05-26 Sihwan Park , Jihun Yun , SungYub Kim , Souvik Kundu , Eunho Yang

Large language models have demonstrated exceptional capabilities across diverse tasks, but their fine-tuning demands significant memory, posing challenges for resource-constrained environments. Zeroth-order (ZO) optimization provides a…

Machine Learning · Computer Science 2025-02-18 Zhen Zhang , Yifan Yang , Kai Zhen , Nathan Susanj , Athanasios Mouchtaris , Siegfried Kunzmann , Zheng Zhang

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

The widespread practice of fine-tuning large language models (LLMs) on domain-specific data faces two major challenges in memory and privacy. First, as the size of LLMs continues to grow, the memory demands of gradient-based training…

Machine Learning · Computer Science 2024-06-07 Liang Zhang , Bingcong Li , Kiran Koshy Thekumparampil , Sewoong Oh , Niao He

Classical optimization theory establishes that zeroth-order (ZO) algorithms suffer from a dimension-dependent slowdown, with convergence rates typically scaling with the model dimension compared to first-order methods. However, in contrast…

Machine Learning · Computer Science 2026-05-06 Zhe Li , Bicheng Ying , Zidong Liu , Haibo Yang

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

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

Zeroth-order (ZO) optimization is a subset of gradient-free optimization that emerges in many signal processing and machine learning applications. It is used for solving optimization problems similarly to gradient-based methods. However, it…

Machine Learning · Computer Science 2020-06-23 Sijia Liu , Pin-Yu Chen , Bhavya Kailkhura , Gaoyuan Zhang , Alfred Hero , Pramod K. Varshney