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

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 Bayesian Subspace Zeroth-Order Optimizer, 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×--1.08× of MeZO).