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This research introduces LlMBO, a gradient-free optimization method that leverages Bayesian techniques to fine-tune large language models with extremely low parameter counts. By avoiding the local search limitations of traditional gradient-based approaches like LoRA, this method achieves comparable or superior accuracy on math benchmarks while significantly reducing compute and memory requirements. The study demonstrates that global optimization becomes tractable in low-dimensional settings, offering a more efficient alternative for resource-constrained fine-tuning scenarios.
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How Low Can You Go: Fine-Tuning LLMs with Bayesian Optimization (LlMBO)

arXiv2 min read

arXiv:2610.18504v1 Announce Type: cross Abstract: Recently, Morris et al. introduced TinyLoRA, a strategy for LLM fine-tuning which introduces arbitrarily few parameters, and demonstrated accuracy improvements using less than $10$ parameters rather than the ${\gtrsim 10,000}$ typically demanded by LoRA-based methods. However, that study continued to use gradient-based local search methods of the kind deployed for training multi-billion parameter LLMs in the first place. This article is predicated on the observation that, in the low dimensional setting, global optimization methods become tractable, unlocking Large language Model Bayesian Optimization (LlMBO). LlMBO is sample-efficient, gradient-free, memory-light, parallelizes across devices without synchronization, and, unlike policy-gradient methods, can optimize greedy-decoding accuracy directly. We describe numerical experiments comparing LlMBO against GRPO on fine-tuning tasks for a variety of models on a math benchmark suite which show that LlMBO can be a suitable alternative in this regime, matching or exceeding GRPO's fine tuning gains, while using a fraction of the compute and memory.

Abstract:Recently, Morris et al. introduced TinyLoRA, a strategy for LLM fine-tuning which introduces arbitrarily few parameters, and demonstrated accuracy improvements using less than $10$ parameters rather than the ${\gtrsim 10,000}$ typically demanded by LoRA-based methods. However, that study continued to use gradient-based local search methods of the kind deployed for training multi-billion parameter LLMs in the first place. This article is predicated on the observation that, in the low dimensional setting, global optimization methods become tractable, unlocking Large language Model Bayesian Optimization (LlMBO). LlMBO is sample-efficient, gradient-free, memory-light, parallelizes across devices without synchronization, and, unlike policy-gradient methods, can optimize greedy-decoding accuracy directly. We describe numerical experiments comparing LlMBO against GRPO on fine-tuning tasks for a variety of models on a math benchmark suite which show that LlMBO can be a suitable alternative in this regime, matching or exceeding GRPO's fine tuning gains, while using a fraction of the compute and memory.

Machine Learning (stat.ML); Machine Learning (cs.LG); Methodology (stat.ME)

arXiv:2610.18504 [stat.ML]

(or arXiv:2610.18504v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2610.18504 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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