# Learning a Zeroth-Order Optimizer for Fine-Tuning LLMs

arXiv: https://arxiv.org/abs/2510.00419 · HTML: https://mlsanity.com/paper/2510.00419/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 47 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Builds on (most cited first, 30 of 34)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [ZOO: Zeroth Order Optimization based Black-box Attacks to Deep Neural Networks without Training Substitute Models](https://mlsanity.com/paper/1708.03999/) (2017)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Learning to Optimize](https://mlsanity.com/paper/1606.01885/) (2016)
- [Adam-mini: Use Fewer Learning Rates To Gain More](https://mlsanity.com/paper/2406.16793/) (2024)
- [Why Transformers Need Adam: A Hessian Perspective](https://mlsanity.com/paper/2402.16788/) (2024)
- [Learned Optimizers that Scale and Generalize](https://mlsanity.com/paper/1703.04813/) (2017)
- [Understanding and correcting pathologies in the training of learned optimizers](https://mlsanity.com/paper/1810.10180/) (2018)
- [Sparse MeZO: Less Parameters for Better Performance in Zeroth-Order LLM Fine-Tuning](https://mlsanity.com/paper/2402.15751/) (2024)
- [Variance-reduced Zeroth-Order Methods for Fine-Tuning Language Models](https://mlsanity.com/paper/2404.08080/) (2024)
- [Second-Order Fine-Tuning without Pain for LLMs:A Hessian Informed Zeroth-Order Optimizer](https://mlsanity.com/paper/2402.15173/) (2024)
- [Learning Gradient Descent: Better Generalization and Longer Horizons](https://mlsanity.com/paper/1703.03633/) (2017)
- [Enhancing Zeroth-order Fine-tuning for Language Models with Low-rank Structures](https://mlsanity.com/paper/2410.07698/) (2024)
- [A Zeroth-Order Block Coordinate Descent Algorithm for Huge-Scale Black-Box Optimization](https://mlsanity.com/paper/2102.10707/) (2021)
- [Learning to Optimize Neural Nets](https://mlsanity.com/paper/1703.00441/) (2017)
- [Practical tradeoffs between memory, compute, and performance in learned optimizers](https://mlsanity.com/paper/2203.11860/) (2022)
- [Zeroth-Order Fine-Tuning of LLMs with Extreme Sparsity](https://mlsanity.com/paper/2406.02913/) (2024)
- [ZO-AdaMU Optimizer: Adapting Perturbation by the Momentum and Uncertainty in Zeroth-order Optimization](https://mlsanity.com/paper/2312.15184/) (2023)

## Built on by (most cited first, 3 of 3)

- [Dominant-Layer ZO: A Single Layer Dominates Zeroth-Order Fine-Tuning of LLMs](https://mlsanity.com/paper/2606.05516/) (2026)
- [Coverage, Not Credit: Failure-Credit Routing of Zeroth-Order Perturbation Budgets Does Not Improve On-Pool Sample Efficiency for LLM Agents](https://mlsanity.com/paper/2608.28011/) (2026)
- [Modular Norm RandOpt: Population-Efficient Ensembling through Architecture-Aware Perturbations](https://mlsanity.com/paper/2609.25745/) (2026)

## Abstract (arXiv)

Zeroth-order optimizers have recently emerged as an attractive approach for fine-tuning large language models (LLMs), as they avoid backpropagation and can substantially reduce memory overhead relative to standard first-order training. However, existing zeroth-order methods rely on hand-crafted, static sampling strategies that are not adaptable to model-specific structures. To address this, we propose ZO-Finetuner, a learning-based zeroth-order optimizer for LLMs that automatically learns efficient perturbation strategies through a compact and memory-efficient design. Motivated by the fact that a small set of base LLMs is repeatedly fine-tuned across tasks, ZO-Finetuner supports one-time per-model training and reuse across downstream tasks with minimal overhead. Therefore, learning the optimizer once for a given LLM and reusing it across diverse downstream tasks is both feasible and highly desirable. Accordingly, ZO-Finetuner is designed to scale learning to learn (L2L) to the foundation-model era by supporting one-time per-model training with minimal overhead. Experiments on 4 LLMs and 7 datasets show that ZO-Finetuner outperforms prior zeroth-order baselines in 82.1% of task-model combinations, thereby demonstrating strong performance and scalability for efficient LLM fine-tuning. The code can be found in https://github.com/ASTRAL-Group/ZOFinetuner.