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Cyber-Physical Systems (CPS) are important components of critical infrastructure and must operate with high levels of reliability and security. We propose a conceptual approach to securing CPSs: the Cyber-Physical Immune System (CPIS), a collection of hardware and software elements deployed on top of a conventional CPS. Inspired by its biological counterpart, the CPIS comprises an independent network of distributed computing units that collects data from the conventional CPS, utilizes data-driven techniques to identify threats, adapts to the changing environment, alerts the user of any threats or anomalies, and deploys threat-mitigation strategies. 

We study the problem of programmatic reinforcement learning, in which policies are represented as short programs in a symbolic language. Programmatic policies can be more interpretable, generalizable, and amenable to formal verification than neural policies; however, designing rigorous learning approaches for such policies remains a challenge. Our approach to this challenge-a meta-algorithm called PROPEL-is based on three insights. First, we view our learning task as optimization in policy space, modulo the constraint that the desired policy has a programmatic representation, and solve this optimization problem using a form of mirror descent that takes a gradient step into the unconstrained policy space and then projects back onto the constrained space. Second, we view the unconstrained policy space as mixing neural and programmatic representations, which enables employing state-of-the-art deep policy gradient approaches. Third, we cast the projection step as program synthesis via imitation learning, and exploit contemporary combinatorial methods for this task. We present theoretical convergence results for PROPEL and empirically evaluate the approach in three continuous control domains. The experiments show that PROPEL can significantly outperform state-of-the-art approaches for learning programmatic policies.