arXiv cs.AI· Swati Gupta, Tianjiao Li·· 2 天前AI 评分22
何时值得为更好的 LLM 付费？混合保真度预言机的随机优化
When is a better LLM worth paying for? Stochastic Optimization with Switching Mixed-Fidelity Oracles
AI 导读
针对 LLM 辅助数据清洗与决策的下游任务，研究提出混合保真度一阶预言机的随机优化框架，用成本感知策略在不同保真度预言机间自适应切换。在偏差已知时，其累积成本不超过事后最优固定预言机；偏差未知时，用预算化认证方案以偶发可信梯度评估剔除有偏来源。合成与 LLM 补全实验显示，该策略跳过多个昂贵 LLM 预言机，在精度相当的情况下大幅降低累积成本。
正文 · 原文
Abstract:Large language models (LLMs) are increasingly used upstream of decision-making to clean data, detect label errors, and reconstruct missing values. Yet LLM-assisted data curation creates a new operational tradeoff: higher-fidelity models and richer prompts can be substantially more expensive, while the value of this additional fidelity depends on the downstream optimization accuracy. This raises the central question of this work: when should one pay for a better LLM, given a specific downstream task at hand?
We study this question through stochastic optimization with mixed-fidelity first-order oracles, which can have systematic bias and state-dependent variance. We develop two cost-aware algorithmic frameworks that allow adaptive switching between stochastic oracles. With known bias, the first meta-algorithm applies a restarted, cost-aware policy that adaptively selects oracle fidelity across optimization stages. Its cumulative cost is no larger than that of the best fixed oracle in hindsight and can be substantially smaller. With unknown bias, we develop a budgeted certification scheme that uses occasional trusted-gradient evaluations to certify the optimization progress and eliminate unsuccessful oracle sources, and show an explicit tradeoff between certification cost and delayed detection of biased sources. We provide concrete realizations of these meta-algorithms by applying biased stochastic gradient extrapolation (SGE) and recursive regularization under state-dependent noise as subroutines. Synthetic and LLM-completion experiments illustrate the qualitative switching behavior predicted by the theory: the adaptive policy skips several expensive LLM oracles and substantially reduces cumulative cost relative to fixed high-fidelity alternatives while achieving comparable accuracy.
| Subjects: | Optimization and Control (math.OC); Artificial Intelligence (cs.AI); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.21139 [math.OC] |
| (or arXiv:2610.21139v1 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2610.21139 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Tianjiao Li [view email]
[v1]
Thu, 15 Oct 2026 02:50:49 UTC (4,598 KB)
来源：arXiv cs.AI · arxiv.org