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

Experience-learning agents for optimization modeling improve by storing verified skills, but existing learners admit knowledge by checking against known answers, which real ticket streams do not provide. The natural label-free alternatives are unreliable: on a 300-problem label-blind stream, admitting every executable model poisons roughly one admission in four, while single-instance agreement accepts models that match at one value but differ elsewhere. We propose AdmitOR, an admission gate built on calibrated external behavioral evidence. Candidates from three model families, prompting strategies, and solver stacks are run on instances resampled from an extracted parameter domain; agreement across the resulting value-function traces is summarized by a cross-family clique, and a calibrated threshold returns accept, abstain, or escalate. The preregistered false-discovery criterion holds on calibration data but not on the wild stream. We report this negative result in full and trace most failures to benchmark texts that do not faithfully encode their labeled instances. Comparing four admission judges on one collection of logs inside a state-of-the-art skill learner, AdmitOR raises admission precision to 0.927, against 0.871 for majority vote and 0.726 for execution success, yielding 3.1x and 8.0x fewer poisoned admissions. Its library is the smallest and attains the highest macro accuracy across five public benchmarks, 58.4 against 54.8 for majority vote and 53.9 for the ground-truth-labeled library. The 3.5-point gain over majority vote is supported by a paired bootstrap and survives correction for a host-side anomaly. To our knowledge, AdmitOR is the first label-free admission mechanism designed around an explicitly calibrated false-discovery target. The transfer failure identifies a necessary condition for extending it to wild streams.

OpenSkill: Open-World Self-Evolution for LLM Agents

Self-evolving agents requires adaptation after deployment, but existing approaches assume a usable learning loop, such as curated skills, successful trajectories, or verifier signals. Real open-world deployments may provide none of these, offering only a task prompt. In this work, we study open-world self-evolution, where an agent must build both its skills and its own verification signals from scratch, using open-world resources but no target-task supervision. We propose OpenSkill, a framework that bootstraps this loop: it acquires grounded knowledge and verification anchors from documentation, repositories, and the web, synthesizes them into transferable skills, and refines those skills against self-built virtual tasks grounded in the anchors rather than in target answers. The open world thus supplies both the knowledge to be learned and a supervision-independent practice environment, with target-task supervision reserved for final evaluation. Across three benchmarks and two target agents, OpenSkill attains the best automated pass rate while satisfying the no-supervision constraint. Analysis shows its skills transfer across models without model-specific adaptation, and its self-built verifier aligns with ground-truth outcomes despite never accessing them.