  Causal discovery from observational data is pivotal for deciphering complex
relationships. Causal Structure Learning (CSL), which focuses on deriving
causal Directed Acyclic Graphs (DAGs) from data, faces challenges due to vast
DAG spaces and data sparsity. The integration of Large Language Models (LLMs),
recognized for their causal reasoning capabilities, offers a promising
direction to enhance CSL by infusing it with knowledge-based causal inferences.
However, existing approaches utilizing LLMs for CSL have encountered issues,
including unreliable constraints from imperfect LLM inferences and the
computational intensity of full pairwise variable analyses. In response, we
introduce the Iterative LLM Supervised CSL (ILS-CSL) framework. ILS-CSL
innovatively integrates LLM-based causal inference with CSL in an iterative
process, refining the causal DAG using feedback from LLMs. This method not only
utilizes LLM resources more efficiently but also generates more robust and
high-quality structural constraints compared to previous methodologies. Our
comprehensive evaluation across eight real-world datasets demonstrates
ILS-CSL's superior performance, setting a new standard in CSL efficacy and
showcasing its potential to significantly advance the field of causal
discovery. The codes are available at
\url{https://github.com/tyMadara/ILS-CSL}.
