Agentic Algorithm Design: LLMs that Propose, Formalise, and Prove Runtime Bounds for Evolutionary Algorithms in Lean· 代理算法设计：LLM 证明进化算法的运行时间边界

LLMs now prove hard theorems in Lean. Can they also design algorithms and prove their correctness and efficiency? LLM-guided design of optimisation heuristics (such as AlphaEvolve) is purely empirical. Automated theorem provers with LLMs prove given statements. So far, there has been little evidence that LLMs can do both: design an algorithm and guarantee its efficiency by a mathematical proof. We present a staged pipeline modelled after research methodology in design and analysis of evolutionary algorithms. The agent proposes black-box optimisation algorithms, and Lean guards filter out flawed designs. The agent then defines a potential function and proves drift bounds that guarantee an expected runtime improvement over the baseline algorithm. At no point in the pipeline are the algorithm