We explore AI-driven distributed-systems policy design by combining stochastic code generation from large language models (LLMs) with deterministic verification in a domain-specific simulator. Using a Function-as-a-Service runtime (Bauplan) and its open-source simulator (Eudoxia) as a case study, we frame scheduler design as an iterative generate-and-verify loop: an LLM proposes a Python policy, the simulator evaluates it on standardized traces, and structured feedback steers subsequent generations. This setup preserves interpretability while enabling targeted search over a large design space. We detail the system architecture and report preliminary results on throughput improvements across multiple models. Beyond early gains, we discuss the limits of the current setup and outline next steps; in particular, we conjecture that AI will be crucial for scaling this methodology by helping to bootstrap new simulators.