  Safety validation is a crucial component in the development and deployment of
autonomous systems, such as self-driving vehicles and robotic systems. Ensuring
safe operation necessitates extensive testing and verification of control
policies, typically conducted in simulation environments. High-fidelity
simulators accurately model real-world dynamics but entail high computational
costs, limiting their scalability for exhaustive testing. Conversely,
low-fidelity simulators offer efficiency but may not capture the intricacies of
high-fidelity simulators, potentially yielding false conclusions. We propose a
joint falsification and fidelity optimization framework for safety validation
of autonomous systems. Our mathematical formulation combines counterexample
searches with simulator fidelity improvement, facilitating more efficient
exploration of the critical environmental configurations challenging the
control system. Our contributions encompass a set of theorems addressing
counterexample sensitivity analysis, sample complexity, convergence, the
interplay between the outer and inner optimization loops, and regret bound
analysis. The proposed joint optimization approach enables a more targeted and
efficient testing process, optimizes the use of available computational
resources, and enhances confidence in autonomous system safety validation.
