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

A new self-improving framework called AlphaOPT enables large language models to learn optimization modeling from limited supervision, according to a paper posted on arXiv. The system accumulates reusable principles through a two-phase cycle without requiring annotated reasoning traces or parameter updates [1][2]. Optimization modeling requires translating natural-language problem descriptions into precise mathematical formulations and executable solver code, a task that remains difficult to automate [2]. Existing approaches that use large language models, or LLMs — neural networks trained on vast text corpora for language tasks — often depend on brittle prompting or expensive retraining, both of which offer limited generalization [2][9]. AlphaOPT addresses these limitations by functioning as a self-improving experience library that learns from solver-verified feedback alone [2]. The system operates in a continual two-phase cycle [1][2]. During the Library Learning phase, AlphaOPT extracts structured insights from failed attempts that have been verified by a solver. The subsequent Library Evolution phase refines the applicability of those stored insights using aggregate evidence gathered across multiple tasks [2]. This design allows the model to accumulate reusable modeling principles, improve transfer across problem instances, and maintain bounded library growth over time [1][2]. Minwei Kong and collaborators evaluated AlphaOPT on multiple optimization benchmarks [1][2]. The model’s accuracy rose from 65% to 72% as the number of training items increased from 100 to 300 [1][2]. On two out-of-distribution datasets, AlphaOPT outperformed the strongest baseline by 9.1% and 8.2%, respectively [1][2]. The authors argue that structured experience learning grounded in solver feedback provides a practical alternative to retraining for complex reasoning tasks that demand precise formulation and execution [2]. The paper was submitted to arXiv on 21 October 2025 and last revised on 7 June 2026 [1]. arXiv is an open-access repository of electronic preprints and postprints that are approved after moderation but not peer reviewed; it hosts papers across mathematics, physics, computer science, and related fields [7]. The code and data for AlphaOPT have been made available on GitHub [1][2].