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Algorithm Discovery With LLMs: Evolutionary Search Meets Reinforcement Learning

Paper · 2025 · Anja Surina, Amin Mansouri, Lars Quaedvlieg et al.

Summary

LLM-driven evolutionary search methods such as FunSearch can discover strong algorithms, but they keep the language model frozen and never learn from what the search finds. Surina et al. (EPFL, Apple) propose EvoTune, which alternates two phases. In the search phase, the model writes Python programs, which are scored on combinatorial optimization instances and stored in an island-based program database. In the training phase, the model is periodically fine-tuned with reinforcement learning, using program scores as rewards. Training uses a DPO-style preference objective applied off-policy to prompts that keep changing. A forward-KL variant of the regularizer helps the generator keep producing varied outputs, which evolutionary exploration depends on. Three instruction-tuned LLMs, ranging from 1B to 3.8B parameters, were evaluated across five task types: symbolic regression, Hash Code challenges, flatpack, traveling salesman routing, and bin packing. Under an equal sampling budget, EvoTune consistently beats FunSearch at finding the best solutions. This suggests that combining search with learning makes automated algorithm design more efficient.

Key points

  • EvoTune's prompts combine m = 2 earlier programs and their scores with a Chain-of-Thought style task description. The base model is updated by RL at fixed intervals during the search.
  • Instead of PPO, the authors use preference optimization (DPO). This avoids training a separate reward model or value function, so it costs less compute.
  • Forward KL regularization keeps the sampled programs diverse. The gains appear in the single best and top-k results, not just in the population's average score.
  • On the Stress-Strain symbolic regression task, EvoTune with Phi-3.5 Mini (3.8B) outperforms baselines built on Mixtral 8x7B and GPT-3.5-turbo. The method also beats several specialized non-LLM methods and human-designed heuristics.
  • Experiments used up to 22.4k samples per run, and the RL phase adds compute cost. The code is open-sourced at claire-labo.github.io/EvoTune.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓École Polytechnique Fédérale de LausanneLausanne · Switzerland56 works · 8,189 citations🏢AppleCupertino · United States25 works · 2,356 citations

 Fields, topics and concepts

📚 Shelves 3The field of science this work belongs to (OpenAlex fields).Computer Science · 19,503 worksArtificial Intelligence · 18,805 worksInformation Systems · 1,888 works

Cite

Cite as Anja Surina, Amin Mansouri, Lars Quaedvlieg, Amal Seddas, Maryna Viazovska, Emmanuel Abbe and Caglar Gulcehre. 2025. Algorithm Discovery With LLMs: Evolutionary Search Meets Reinforcement Learning. arXiv:2504.05108.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2504.05108 · arXiv 2504.05108

@misc{surina2025algorithm,
  title = {{Algorithm Discovery With LLMs: Evolutionary Search Meets Reinforcement Learning}},
  author = {Anja Surina, Amin Mansouri, Lars Quaedvlieg, Amal Seddas, Maryna Viazovska, Emmanuel Abbe and Caglar Gulcehre},
  year = {2025},
  doi = {10.48550/arxiv.2504.05108},
  eprint = {2504.05108},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2504.05108}
}

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