Towards Theoretical Understanding of Data-Driven Policy Refinement

This paper presents an approach for data-driven policy refinement in reinforcement learning, specifically designed for safety-critical applications. Our methodology leverages the strengths of data-driven optimization and reinforcement learning to enhance policy safety and optimality through iterative refinement. Our principal contribution lies in the mathematical formulation of this data-driven policy refinement concept. This framework systematically improves reinforcement learning policies by learning from counterexamples surfaced during data-driven verification. Furthermore, we present a series of theorems elucidating key theoretical properties of our approach, including convergence, robustness bounds, generalization error, and resilience to model mismatch. These results not only validate the effectiveness of our methodology but also contribute to a deeper understanding of its behavior in different environments and scenarios.