Admission Without Answers: Label-Free Certification and Experience Learning for LLM-Based Optimization Modeling

TL;DR - AdmitOR is a label-free gate for deciding which optimization-modeling skills an LLM agent should retain. It improves admission precision and downstream benchmark accuracy, while exposing limitations when benchmark descriptions misrepresent labeled instances.

• Compares value-function traces across resampled parameter instances, model families, prompts, and solver stacks.
• Achieves 0.927 admission precision versus 0.871 for majority vote and 0.726 for execution-only checks.
• Its smaller skill library reaches 58.4 macro accuracy across five benchmarks, outperforming majority vote at 54.8 and a ground-truth-labeled library at 53.9.
• Its calibrated false-discovery criterion fails on a wild stream, largely because some benchmark texts do not faithfully encode their labeled instances.