Robust and Efficient Zeroth-Order LLM Fine-Tuning via Adaptive Bayesian Subspace Optimizer
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909991887175680 |
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| author | Feng, Jian Huang, Zhihong |
| author_facet | Feng, Jian Huang, Zhihong |
| contents | Fine-tuning large language models (LLMs) with zeroth-order (ZO) optimization reduces memory by approximating gradients through function evaluations. However, existing methods essentially perform updates in a one-dimensional space, and suffer from collapse or substantial performance degradation under low-precision training. We introduce BSZO, an adaptive \textbf{B}ayesian \textbf{S}ubspace \textbf{Z}eroth-Order \textbf{O}ptimizer, which applies Kalman filtering to combine finite-difference information across multiple perturbation directions within a subspace. By treating each finite-difference measurement as a noisy observation, BSZO builds a posterior distribution over the subspace-projected gradient and updates it through Bayesian inference, with a residual-based adaptive mechanism to adapt to noise variations. Theoretical analysis shows that BSZO improves the convergence rate by a factor of $k/γ$ compared to standard ZO methods. Experiments on RoBERTa, Mistral, and OPT models show that BSZO outperforms the baselines across various tasks, achieving up to 6.67\% absolute average improvement on OPT-13B while remaining robust under fp16/bf16 precision and keeping memory usage close to inference-only baselines (1.00$\times$--1.08$\times$ of MeZO). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01452 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust and Efficient Zeroth-Order LLM Fine-Tuning via Adaptive Bayesian Subspace Optimizer Feng, Jian Huang, Zhihong Machine Learning Artificial Intelligence Fine-tuning large language models (LLMs) with zeroth-order (ZO) optimization reduces memory by approximating gradients through function evaluations. However, existing methods essentially perform updates in a one-dimensional space, and suffer from collapse or substantial performance degradation under low-precision training. We introduce BSZO, an adaptive \textbf{B}ayesian \textbf{S}ubspace \textbf{Z}eroth-Order \textbf{O}ptimizer, which applies Kalman filtering to combine finite-difference information across multiple perturbation directions within a subspace. By treating each finite-difference measurement as a noisy observation, BSZO builds a posterior distribution over the subspace-projected gradient and updates it through Bayesian inference, with a residual-based adaptive mechanism to adapt to noise variations. Theoretical analysis shows that BSZO improves the convergence rate by a factor of $k/γ$ compared to standard ZO methods. Experiments on RoBERTa, Mistral, and OPT models show that BSZO outperforms the baselines across various tasks, achieving up to 6.67\% absolute average improvement on OPT-13B while remaining robust under fp16/bf16 precision and keeping memory usage close to inference-only baselines (1.00$\times$--1.08$\times$ of MeZO). |
| title | Robust and Efficient Zeroth-Order LLM Fine-Tuning via Adaptive Bayesian Subspace Optimizer |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2601.01452 |