arXiv：cs.AI· Yuhua Qian·· 18 小时前
用原始-对偶证书审计 LLM 程序搜索求解 Bermudan 期权停止问题
Auditing LLM Program Search for Bermudan Stopping with Primal--Dual Certificates
AI 导读
一项被 NeurIPS 2026 MATH-AI Workshop 接收的研究用原始-对偶证书审计 LLM 驱动的 Python 策略搜索求解 Bermudan 期权最优停止问题，对两个流程的 24 次生成尝试、六组反馈-表示消融及冻结选择后的留出集进行评估，发现没有生成的程序能稳定或超出蒙特卡洛误差地优于 Ridge LSMC，留出集差距分数在其 0.002 以内。
正文
Abstract:LLM program-search agents are usually judged by the score that drives their search. We study LLM-driven search over Python exercise policies for Bermudan options, an optimal stopping problem where a trusted evaluator owns the simulation and a dual upper bound~$U$. For any policy, $0 \le V^\star - L_\pi \le U - L_\pi$; we report Monte Carlo estimates of both bounds with their sampling error. We audit 24 generation attempts from two pipelines, a six-pair feedback-representation ablation, and a holdout evaluated after selection was frozen. No selected generated program improves on Ridge LSMC consistently or by more than Monte Carlo uncertainty; holdout gap scores lie within $0.002$ of it. On six one-dimensional puts, a high-precision binomial reference places Ridge within Monte Carlo noise of optimal and attributes 99\% of the estimated gap to dual-bound looseness, so this dual audits validity but cannot certify progress at the search's scale. Structured memory showed no benefit over score-only memory in this ablation. Whether search ``worked'' depends on reporting rules: retaining the initial reference, freezing selection before holdout, and counting failures.
| Comments: | Accepted at the MATH-AI Workshop at NeurIPS 2026 |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| MSC classes: | 60G40, 91G60, 68T05 |
| ACM classes: | I.2.6; I.2.2 |
| Cite as: | arXiv:2610.14063 [cs.LG] |
| (or arXiv:2610.14063v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.14063 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Yuhua Qian [view email]
[v1]
Wed, 7 Oct 2026 09:00:25 UTC (67 KB)
来源：arXiv：cs.AI · arxiv.org