@inproceedings{tan-etal-2026-grzo,
title = "{GRZO}: Group-Relative Zeroth-Order Optimization for Large Language Model Fine-Tuning",
author = "Tan, Liyan and
Zhao, Yequan and
Yang, Yifan and
Zhang, Ruijie and
Yu, Xinling and
Zhang, Zheng",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {EMNLP} 2026",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-emnlp.1711/",
pages = "36551--36581",
ISBN = "979-8-89176-462-0",
abstract = "Zeroth-order (ZO) optimization is a memory-efficient alternative to backpropagation for fine-tuning large language models, but its deployment is limited by the high variance of gradient estimation. We propose **GRZO**, a **G**roup-**R**elative **Z**eroth-**O**rder optimizer that draws one pseudo-independent perturbation per mini-batch example and aggregates the per-example losses through group-relative normalization, raising the effective gradient-direction count from one to the batch size at no additional forward cost while preserving inference-level memory. We prove that GRZO is directionally unbiased with variance shrinking proportionally to the batch size, yielding a tighter nonconvex convergence bound than MeZO. Across RoBERTa-large, Llama3-8B, and OPT-13B over multiple tasks, GRZO improves average accuracy on Llama3-8B by $+3.0$ over MeZO while staying within 0.5{\%} of the forward-only inference memory floor; as a drop-in replacement for the MeZO core, it lifts sparse, low-rank, and quantized ZO variants by $+4.9$ on average."
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<abstract>Zeroth-order (ZO) optimization is a memory-efficient alternative to backpropagation for fine-tuning large language models, but its deployment is limited by the high variance of gradient estimation. We propose **GRZO**, a **G**roup-**R**elative **Z**eroth-**O**rder optimizer that draws one pseudo-independent perturbation per mini-batch example and aggregates the per-example losses through group-relative normalization, raising the effective gradient-direction count from one to the batch size at no additional forward cost while preserving inference-level memory. We prove that GRZO is directionally unbiased with variance shrinking proportionally to the batch size, yielding a tighter nonconvex convergence bound than MeZO. Across RoBERTa-large, Llama3-8B, and OPT-13B over multiple tasks, GRZO improves average accuracy on Llama3-8B by +3.0 over MeZO while staying within 0.5% of the forward-only inference memory floor; as a drop-in replacement for the MeZO core, it lifts sparse, low-rank, and quantized ZO variants by +4.9 on average.</abstract>
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%0 Conference Proceedings
%T GRZO: Group-Relative Zeroth-Order Optimization for Large Language Model Fine-Tuning
%A Tan, Liyan
%A Zhao, Yequan
%A Yang, Yifan
%A Zhang, Ruijie
%A Yu, Xinling
%A Zhang, Zheng
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F tan-etal-2026-grzo
%X Zeroth-order (ZO) optimization is a memory-efficient alternative to backpropagation for fine-tuning large language models, but its deployment is limited by the high variance of gradient estimation. We propose **GRZO**, a **G**roup-**R**elative **Z**eroth-**O**rder optimizer that draws one pseudo-independent perturbation per mini-batch example and aggregates the per-example losses through group-relative normalization, raising the effective gradient-direction count from one to the batch size at no additional forward cost while preserving inference-level memory. We prove that GRZO is directionally unbiased with variance shrinking proportionally to the batch size, yielding a tighter nonconvex convergence bound than MeZO. Across RoBERTa-large, Llama3-8B, and OPT-13B over multiple tasks, GRZO improves average accuracy on Llama3-8B by +3.0 over MeZO while staying within 0.5% of the forward-only inference memory floor; as a drop-in replacement for the MeZO core, it lifts sparse, low-rank, and quantized ZO variants by +4.9 on average.
%U https://aclanthology.org/2026.findings-emnlp.1711/
%P 36551-36581
Markdown (Informal)
[GRZO: Group-Relative Zeroth-Order Optimization for Large Language Model Fine-Tuning](https://aclanthology.org/2026.findings-emnlp.1711/) (Tan et al., Findings 2026)
ACL