GRZO: Group-Relative Zeroth-Order Optimization for Large Language Model Fine-Tuning

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 Group-Relative Zeroth-Order 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 at $23\%$ lower peak GPU memory; as a drop-in replacement for the MeZO core, it lifts sparse, low-rank, and quantized ZO variants by $+6.0$ on average.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2606.02857 [cs.LG]

(or arXiv:2606.02857v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.02857 Focus to learn more arXiv-issued DOI via DataCite

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