Robust and Efficient Zeroth-Order LLM Fine-Tuning via Adaptive Bayesian Subspace Optimizer

• URL: http://arxiv.org/abs/2601.01452v2
• Date: Mon, 12 Jan 2026 11:20:01 GMT
• Title: Robust and Efficient Zeroth-Order LLM Fine-Tuning via Adaptive Bayesian Subspace Optimizer
• Authors: Jian Feng, Zhihong Huang,
• Abstract summary: Fine-tuning large language models (LLMs) with zeroth-order (ZO) optimization reduces memory by approximating gradients through function evaluations.<n>We introduce BSZO, an adaptive textbfBayesian textbfSubspace textbfZeroth-Order textbfOptimizer.
• Score: 4.6561758107970395
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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).

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