FactorSmith: Agentic Simulation Generation via Markov Decision Process Decomposition with Planner-Designer-Critic Refinement

Generating executable simulations from natural language specifications remains a challenging problem due to the limited reasoning capacity of large language models (LLMs) when confronted with large, interconnected codebases. This paper presents FactorSmith, a framework that synthesizes playable game simulations in code from textual descriptions by combining two complementary ideas: factored POMDP decomposition for principled context reduction and a hierarchical planner-designer-critic agentic workflow for iterative quality refinement at every generation step. Drawing on the factored partially observable Markov decision process (POMDP) representation introduced by FactorSim [Sun et al., 2024], the proposed method decomposes a simulation specification into modular steps where each step operates only on a minimal subset of relevant state variables, limiting the context window that any single LLM call must process. Inspired by the agentic trio architecture of SceneSmith [Pfaff et al., 2025], FactorSmith embeds within every factored step a three-agent interaction: a planner that orchestrates workflow, a designer that proposes code artifacts, and a critic that evaluates quality through structured scoring, enabling iterative refinement with checkpoint rollback. This paper formalizes the combined approach, presents the mathematical framework underpinning context selection and agentic refinement, and describes the open-source implementation. Experiments on the PyGame Learning Environment benchmark demonstrate that FactorSmith generates simulations with improved prompt alignment, fewer runtime errors, and higher code quality compared to non-agentic factored baselines.