Combining Large Language Models and Gradient-Free Optimization for Automatic Control Policy Synthesis

Large Language models (LLMs) have shown promise as generators of symbolic control policies, producing interpretable program-like representations through iterative search. However, these models are not capable of separating the functional structure of a policy from the numerical values it is parametrized by, thus making the search process slow and inefficient. We propose a hybrid approach that decouples structural synthesis from parameter optimization by introducing an additional optimization layer for local parameter search. In our method, the numerical parameters of LLM-generated programs are extracted and optimized numerically to maximize task performance. With this integration, an LLM iterates over the functional structure of programs, while a separate optimization loop is used to find a locally optimal set of parameters accompanying candidate programs. We evaluate our method on a set of control tasks, showing that it achieves higher returns and improved sample efficiency compared to purely LLM-guided search. We show that combining symbolic program synthesis with numerical optimization yields interpretable yet high-performing policies, bridging the gap between language-model-guided design and classical control tuning. Our code is available at https://sites.google.com/berkeley.edu/colmo.