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Recent developments in surrogate construction predominantly focused on two strategies to improve surrogate accuracy. Firstly, component-wise domain scaling informed by cross-validation. Secondly, regression to construct response surfaces…

Optimization and Control · Mathematics 2023-04-03 Johann Bouwer , Daniel N. Wilke , Schalk Kok

Parameter-efficient fine-tuning (PEFT) significantly reduces memory costs when adapting large language models (LLMs) for downstream applications. However, traditional first-order (FO) fine-tuning algorithms incur substantial memory overhead…

Machine Learning · Computer Science 2024-10-11 Yiming Chen , Yuan Zhang , Liyuan Cao , Kun Yuan , Zaiwen Wen

Zeroth-Order (ZO) optimization has emerged as a promising solution for fine-tuning LLMs under strict memory constraints, as it avoids the prohibitive memory cost of storing activations for backpropagation. However, existing ZO methods…

Machine Learning · Computer Science 2026-05-25 Wei Lin , Yining Jiang , Qingyu Song , Qiao Xiang , Hong Xu

In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we make two main contributions. First, we…

Machine Learning · Statistics 2013-05-15 Julien Mairal

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

Zeroth-order (ZO, also known as derivative-free) methods, which estimate the gradient only by two function evaluations, have attracted much attention recently because of its broad applications in machine learning community. The two function…

Machine Learning · Computer Science 2021-04-12 Zhou Zhai , Bin Gu , Heng Huang

This paper considers a consensus optimization problem, where all the nodes in a network, with access to the zeroth-order information of its local objective function only, attempt to cooperatively achieve a common minimizer of the sum of…

Optimization and Control · Mathematics 2024-06-17 Chengan Wang , Zichong Ou , Jie Lu

Surrogate Optimization (SO) algorithms have shown promise for optimizing expensive black-box functions. However, their performance is heavily influenced by hyperparameters related to sampling and surrogate fitting, which poses a challenge…

Machine Learning · Computer Science 2023-10-13 Nazanin Nezami , Hadis Anahideh

Recently introduced distributed zeroth-order optimization (ZOO) algorithms have shown their utility in distributed reinforcement learning (RL). Unfortunately, in the gradient estimation process, almost all of them require random samples…

Systems and Control · Electrical Eng. & Systems 2024-05-06 Gangshan Jing , He Bai , Jemin George , Aranya Chakrabortty , Piyush K. Sharma

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

Derivative-Free Optimization (DFO) involves methods that rely solely on evaluations of the objective function. One of the earliest strategies for designing DFO methods is to adapt first-order methods by replacing gradients with…

Optimization and Control · Mathematics 2025-02-12 Timothé Taminiau , Estelle Massart , Geovani Nunes Grapiglia

Online bilevel optimization (OBO) is a powerful framework for machine learning problems where both outer and inner objectives evolve over time, requiring dynamic updates. Current OBO approaches rely on deterministic \textit{window-smoothed}…

Machine Learning · Computer Science 2026-05-20 Parvin Nazari , Bojian Hou , Davoud Ataee Tarzanagh , Li Shen , George Michailidis

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

Zeroth-Order Optimization (ZOO) provides powerful tools for optimizing functions where explicit gradients are unavailable or expensive to compute. However, the underlying mechanisms of popular ZOO methods, particularly those employing…

Machine Learning · Computer Science 2025-06-18 Junbin Qiu , Zhengpeng Xie , Xiangda Yan , Yongjie Yang , Yao Shu

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

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

In this paper, we consider a stochastic distributed nonconvex optimization problem with the cost function being distributed over $n$ agents having access only to zeroth-order (ZO) information of the cost. This problem has various machine…

Optimization and Control · Mathematics 2022-01-11 Xinlei Yi , Shengjun Zhang , Tao Yang , Karl H. Johansson

This paper investigates how to accelerate the convergence of distributed optimization algorithms on nonconvex problems with zeroth-order information available only. We propose a zeroth-order (ZO) distributed primal-dual stochastic…

Optimization and Control · Mathematics 2021-10-15 Shengjun Zhang , Colleen P. Bailey

Zeroth-order (ZO) optimization enables memory-efficient training of neural networks by estimating gradients via forward passes only, eliminating the need for backpropagation. However, the stochastic nature of gradient estimation…

Machine Learning · Computer Science 2026-03-24 Chen Zhang , Yuxin Cheng , Chenchen Ding , Shuqi Wang , Jingreng Lei , Runsheng Yu , Yik-Chung WU , Ngai Wong

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