Auto-Formulating Dynamic Programming Problems with Large Language Models
Summary: arXiv:2507.11737v2 Announce Type: replace
Abstract: Dynamic programming (DP) is a fundamental method in operations research, but formulating DP models has traditionally required expert knowledge of both the problem context and DP techniques. Large Language Models (LLMs) offer the potential to automate this process. However, DP problems pose unique challenges due to their inherently stochastic transitions and the limited availability of training data. These factors make it difficult to directly apply existing LLM-based models or frameworks developed for other optimization problems, such as linear or integer programming. We introduce DP-Bench, the first benchmark covering a wide range of textbook-level DP problems to enable systematic evaluation. We present Dynamic Programming Language Model (DPLM), a 7B-parameter specialized model that achieves performance comparable to state-of-the-art LLMs like OpenAI’s o1 and DeepSeek-R1, and surpasses them on hard problems. Central to DPLM’s effectiveness is DualReflect, our novel synthetic data generation pipeline, designed to scale up training data from a limited set of initial examples. DualReflect combines forward generation for diversity and backward generation for reliability. Our results reveal a key insight: backward generation is favored in low-data regimes for its strong correctness guarantees, while forward generation, though lacking such guarantees, becomes increasingly valuable at scale for introducing diverse formulations. This trade-off highlights the complementary strengths of both approaches and the importance of combining them.
Key Insights and Innovations
The introduction of DP-Bench and DPLM marks a significant advancement in the field of dynamic programming and artificial intelligence. The following points summarize the key insights and innovations presented in the research:
- DP-Bench: A comprehensive benchmark that encompasses a variety of textbook-level dynamic programming problems, allowing for systematic evaluation of LLM capabilities in this domain.
- DPLM Model: A specialized 7B-parameter model designed to tackle dynamic programming problems, achieving performance levels comparable to leading LLMs while excelling in more complex scenarios.
- DualReflect Pipeline: A novel synthetic data generation approach that enhances the training dataset for DPLM, utilizing both forward and backward generation techniques.
- Backward Generation Strategy: Proven to be more effective in low-data environments, offering robust correctness guarantees essential for reliable model outputs.
- Forward Generation Strategy: While less reliable, it fosters diversity in problem formulation, becoming increasingly beneficial as the dataset expands.
Implications for Operations Research
The ability to automatically formulate dynamic programming problems has several implications for the field of operations research and beyond:
- Increased Accessibility: By reducing the requirement for expert knowledge, the research democratizes access to dynamic programming methodologies, enabling more practitioners to leverage these techniques.
- Enhanced Problem-Solving: The automation of problem formulation can lead to faster and more efficient solutions in various applications, from logistics to finance.
- Future Research Directions: The findings open avenues for further exploration in machine learning and operations research, particularly in how LLMs can be adapted for various optimization problems.
Conclusion
In summary, the integration of large language models in the formulation of dynamic programming problems presents a transformative opportunity for the field of operations research. The development of DP-Bench and DPLM, along with the innovative DualReflect pipeline, sets the stage for more efficient problem-solving methods that can significantly enhance the capabilities of practitioners in diverse industries.