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Emerging applications in artificial intelligence, such as driverless cars and autonomous aircraft promise to be more efficient, cheaper to operate, and always available. However, ensuring the safety of these systems remains a major challenge to their certification and adoption. These autonomous systems are expected to routinely make safety-critical decisions where failures can have serious consequences including loss of life and property. Testing and validation techniques aim to identify and diagnose potential failures before the system is deployed. However, finding failure scenarios in autonomous systems can be very challenging due to high-dimensional and continuous state spaces, interaction with large environments over many time steps, and the rarity of failures. This talk presents Adaptive Stress Testing (AST), a simulation-based testing framework for finding the most likely path to a failure event of a safety-critical system. The key idea of AST is that stress testing can be formulated as a Partially Observable Markov Decision Process (POMDP), which enables reinforcement learning techniques to be used for finding failure events. Reinforcement learning algorithms can efficiently explore the search space and have been shown to scale to very large systems. We present applications of AST to find failures in various safety-critical systems including the aircraft collision avoidance systems, autonomous cars, and small unmanned aerial vehicles.