Optimizing the Cost-Quality Tradeoff of Agentic Theorem Provers in Lean

The article presents an action routing agent designed to optimize the cost-quality tradeoff in generating formal proofs using Lean, a formal proof assistant. The agent features a data plane for lemma decomposition and proof attempt sampling, and a control plane that leverages feedback from previous attempts to estimate success likelihood and costs. On a subset of PutnamBench, the agent achieved a 28.9% reduction in compute costs compared to a fixed-step baseline while maintaining proof performance, highlighting the potential for improved resource allocation in theorem proving workflows.