Admission Without Answers: Label-Free Certification and Experience Learning for LLM-Based Optimization Modeling
ADMITOR enhances optimization modeling precision with label-free certification, achieving candidate precision of 0.927.
Key Findings
Methodology
ADMITOR is a label-free certification method that generates candidate models from three model families, runs each on resampled parameter instances, and selects the largest group of models whose optimal values agree across all instances. It applies a threshold fitted on solver-verified problems to accept, abstain, or escalate, controlling the false discovery rate among accepted values.
Key Results
- ADMITOR achieves candidate-level admission precision of 0.927, compared to 0.871 for majority vote and 0.726 for execution success.
- On five public benchmarks, ADMITOR's macro accuracy reaches 58.4, compared to 54.8 for majority vote.
- Ablation studies show the gain comes from the accepted value being external to the learner and unanimous across families.
Significance
ADMITOR improves the accuracy of optimization modeling through label-free certification, particularly in streams of new problems without ground-truth labels. It addresses the risk of repeated use of incorrect trajectories in existing methods and demonstrates superior performance across multiple benchmarks.
Technical Contribution
ADMITOR introduces a novel label-free certification mechanism that selects models based on cross-family consistency. This approach provides a finite-sample bound on the false discovery rate and demonstrates high precision and efficiency in experiments.
Novelty
ADMITOR is the first to certify optimization models in a label-free environment through cross-family consistency, offering a fundamental innovation compared to existing label-dependent systems.
Limitations
- The false discovery bound does not hold on the benchmark stream, mainly due to missing or rounded numbers needed to reproduce labeled answers in benchmark texts.
- Resampling never changed an accepted value but reduced coverage.
Future Work
Future work could explore validating ADMITOR's effectiveness on more diverse benchmarks and investigate further reduction of the false discovery rate.
AI Executive Summary
In optimization modeling, once an incorrect trajectory is stored, it can be repeatedly used, affecting subsequent decisions. Existing methods rely on matching known optima or labels to avoid this risk, but real-world problem streams often lack reliable answers. ADMITOR addresses this issue through label-free certification. It generates candidate models from different families, runs them on resampled parameter instances, and selects the largest group with consistent optimal values across all instances. Experiments show ADMITOR excels across multiple benchmarks, achieving candidate-level admission precision of 0.927 and macro accuracy of 58.4. Although the false discovery bound does not hold on the benchmark stream, ADMITOR still demonstrates potential and value in optimization modeling. Future research could explore its application in more diverse scenarios.
Deep Analysis
Background
Optimization modeling translates natural language descriptions of operational problems into executable models. Recent advances in experience learning improve modeling capabilities by storing and reusing solved trajectories. However, incorrect trajectories can be repeatedly used, affecting subsequent decisions.
Core Problem
In real-world problem streams, the lack of ground-truth labels makes it difficult for existing methods to avoid the repeated use of incorrect trajectories. This label wall limits the accuracy and efficiency of optimization modeling.
Innovation
ADMITOR addresses the label wall by certifying optimization models through label-free methods. It generates candidate models from different families and runs them on resampled parameter instances, selecting the largest group with consistent optimal values.
Methodology
- �� Generate candidate models from three model families
- �� Run each model on resampled parameter instances
- �� Select the largest group with consistent optimal values across all instances
- �� Apply a threshold fitted on solver-verified problems to accept, abstain, or escalate
Experiments
Experiments used five public benchmarks to compare ADMITOR with majority vote and execution success. Key metrics include candidate-level admission precision and macro accuracy.
Results
ADMITOR achieves candidate-level admission precision of 0.927 and macro accuracy of 58.4, outperforming majority vote and execution success.
Applications
ADMITOR can be applied in scenarios requiring high-precision optimization modeling, such as supply chain management and resource allocation. Its label-free certification mechanism helps improve model accuracy in the absence of ground-truth labels.
Limitations & Outlook
The false discovery bound does not hold on the benchmark stream, mainly due to missing or rounded numbers needed to reproduce labeled answers in benchmark texts. Future research could explore reducing the false discovery rate.
Plain Language Accessible to non-experts
Imagine you work in a library, selecting which books to add to the collection. You don't have time to read each book, so you rely on the cover and summary. ADMITOR acts like a smart assistant, gathering opinions from different reviewers and only adding a book to the collection if all reviewers agree it's worth it. This ensures the quality of the collection, even without detailed reviews.
ELI14 Explained like you're 14
Imagine you're playing a game where you need to choose the best gear to defeat enemies. You don't have time to test each piece of gear, so you rely on its appearance and description. ADMITOR is like a smart assistant, gathering opinions from different players and only choosing gear if all players agree it's worth using. This ensures you pick the best gear, even without detailed testing.
Glossary
ADMITOR (Label-Free Certification)
A label-free certification method that selects optimization models based on cross-family consistency.
Used to improve optimization modeling accuracy.
False Discovery Rate
The proportion of incorrect values among accepted ones.
Used to evaluate ADMITOR's performance.
Model Family
A set of models using different strategies and solvers.
ADMITOR uses multiple model families to enhance certification reliability.
Resampled Parameter Instance
Instances rerun under different parameters.
Used to test model consistency under varying conditions.
Macro Accuracy
Average accuracy across multiple benchmarks.
Used to evaluate ADMITOR's overall performance.
Open Questions Unanswered questions from this research
- 1 How to validate ADMITOR's effectiveness on more diverse benchmarks?
- 2 How to further reduce ADMITOR's false discovery rate?
Applications
Immediate Applications
Supply Chain Management
ADMITOR can optimize resource allocation in supply chains, improving efficiency and accuracy.
Long-term Vision
Automated Decision Systems
ADMITOR's label-free certification mechanism can be applied to automated decision systems, enhancing adaptability in complex environments.
Abstract
Agents that learn from experience improve at optimization modeling by storing solved trajectories and reusing them as skills. A wrong trajectory that enters the library can be retrieved again and again, and on a stream of new problems there is no ground-truth answer to decide with. Existing learners admit trajectories by matching known optima or labels, and label-free substitutes such as execution success or agreement at one instance can admit wrong models. We introduce ADMITOR, a label-free admission gate. It generates models from three model families, runs each on the stated problem and on instances with resampled parameters, keeps the largest group of models whose optimal values agree on every instance across families, and applies a threshold fitted on solver-verified problems to accept, abstain, or escalate, with a finite-sample bound on the false-discovery rate among accepted values. Inside a state-of-the-art skill learner, ADMITOR raises candidate-level admission precision to 0.927, against 0.871 for majority vote over the host's own samples and 0.726 for execution success, and its library, the smallest of the four, reaches the highest macro accuracy over five public benchmarks, 58.4 against 54.8 for majority vote. An ablation on the same records shows that the gain comes from the accepted value being external to the learner and unanimous across families; on this stream, resampling never changed an accepted value and only reduced coverage. The false-discovery bound holds on the calibration set but not on the benchmark stream: an audit of every false certificate traces most of them to benchmark texts that omit or round the numbers needed to reproduce the labeled answer, and a label-free check of the extracted numbers against the text flags most of these cases.