  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 identified 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.
