This work formalizes the hybrid LLM-planner and RL-controller architecture as a Goal-Augmented Markov Decision Process and shows that when the LLM per-state progress score is used as a bounded potential function, the resulting shaping term preserves the optimal policy set even when the LLM scores are inaccurate.
Abstract
Combining large language models with reinforcement learning is increasingly explored, yet the theoretical status of LLM-derived reward signals is often left implicit. We formalize the hybrid LLM-planner and RL-controller architecture as a Goal-Augmented Markov Decision Process and show that when the LLM per-state progress score is used as a bounded potential function, the resulting shaping term preserves the optimal policy set even when the LLM scores are inaccurate. This guarantee is stronger than what general LLM-as-reward approaches provide. We verify the result numerically on a small MDP under four potential configurations, including an adversarial one scaled to twenty times the base reward magnitude.
A novel policy gradient method is introduced, Hindsight Policy Optimization (HPO), that projects both the current policy distribution and the hindsight distribution into an intent space and extracts low-variance learning signals from the Wasserstein distance between them.
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