AlphaOPT: Formulating Optimization Programs with Self-Improving LLM Experience Library

2025-10-21

AI Summary

Automating the translation of informal optimization requirements into formal mathematical models and executable solver code remains a significant challenge. Method: This paper proposes a two-stage self-evolving framework. In Stage I, a large language model (LLM) leverages solver feedback and retrieval-augmented generation to construct a structured experience repository—without labeled demonstrations, using only ground-truth solutions. In Stage II, knowledge is extracted from failure cases to dynamically refine applicability conditions, enabling explicit, interpretable, and fine-tuning-free continual learning. Contribution/Results: The core innovation lies in modeling experience repository evolution as a condition-driven self-improvement process, supporting cross-task generalization. Evaluated on OptiBench, our method outperforms the strongest baseline by 7.7%. Accuracy improves from 65% to 72% as training samples increase from 100 to 300, demonstrating both effectiveness and scalability.

Technology Category

• Search and Optimization: Learning to Search
• Intelligent Robots: Learning & Optimization for ROB
• Machine Learning: Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Optimization modeling enables critical decisions across industries but remains difficult to automate: informal language must be mapped to precise mathematical formulations and executable solver code. Prior LLM approaches either rely on brittle prompting or costly retraining with limited generalization. We present AlphaOPT, a self-improving experience library that enables an LLM to learn from limited demonstrations (even answers alone, without gold-standard programs) and solver feedback - without annotated reasoning traces or parameter updates. AlphaOPT operates in a continual two-phase cycle: (i) a Library Learning phase that reflects on failed attempts, extracting solver-verified, structured insights as {taxonomy, condition, explanation, example}; and (ii) a Library Evolution phase that diagnoses retrieval misalignments and refines the applicability conditions of stored insights, improving transfer across tasks. This design (1) learns efficiently from limited demonstrations without curated rationales, (2) expands continually without costly retraining by updating the library rather than model weights, and (3) makes knowledge explicit and interpretable for human inspection and intervention. Experiments show that AlphaOPT steadily improves with more data (65% to 72% from 100 to 300 training items) and surpasses the strongest baseline by 7.7% on the out-of-distribution OptiBench dataset when trained only on answers. Code and data are available at: https://github.com/Minw913/AlphaOPT.

Problem

• Automating optimization modeling from informal language to mathematical formulations
• Learning from limited demonstrations without annotated reasoning traces
• Continually improving performance without costly model retraining through experience library

Innovation

• Self-improving experience library learns from limited demonstrations and solver feedback
• Two-phase cycle with library learning and evolution without model retraining
• Explicit interpretable knowledge enables human inspection and intervention