The desire to use reinforcement learning in safety-critical settings has inspired a recent interest in formal methods for learning algorithms. Existing formal methods for learning and optimization primarily consider the problem of constrained learning or constrained optimization. Given a single correct model and associated safety constraint, these approaches guarantee efficient learning while provably avoiding behaviors outside the safety constraint. Acting well given an accurate environmental model is an important pre-requisite for safe learning, but is ultimately insufficient for systems that operate in complex heterogeneous environments. This paper introduces verification-preserving model updates, the first approach toward obtaining formal safety guarantees for reinforcement learning in settings where multiple possible environmental models must be taken into account. Through a combination of inductive data and deductive proving with design-time model updates and runtime model falsification, we provide a first approach toward obtaining formal safety proofs for autonomous systems acting in heterogeneous environments.
propose an approach, based on deep reinforcement learning, for efficiently discovering defects in models of cyber-physical systems with specifications stated in signal temporal logic @cite_2 . Model falsification is an important component of our approach; however, unlike , we also propose an approach toward obtaining more robust models and explain how runtime falsification can be used to obtain safety guarantees for off-model learning.
@cite_2
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This paper introduces a framework for inference of timed temporal logic properties from data. The dataset is given as a finite set of pairs of finite-time system traces and labels, where the labels indicate whether the traces exhibit some desired behavior (e.g., a ship traveling along a safe route). We propose a decision-tree based approach for learning signal temporal logic classifiers. The method produces binary decision trees that represent the inferred formulae. Each node of the tree contains a test associated with the satisfaction of a simple formula, optimally tuned from a predefined finite set of primitives. Optimality is assessed using heuristic impurity measures, which capture how well the current primitive splits the data with respect to the traces' labels. We propose extensions of the usual impurity measures from machine learning literature to handle classification of system traces by leveraging upon the robustness degree concept. The proposed incremental construction procedure greatly improves the execution time and the accuracy compared to existing algorithms. We present two case studies that illustrate the usefulness and the computational advantages of the algorithms. The first is an anomaly detection problem in a maritime environment. The second is a fault detection problem in an automotive powertrain system. With the rapid development of software and distributed computing, Cyber-Physical Systems (CPS) are widely adopted in many application areas, e.g., smart grid, autonomous automobile. It is difficult to detect defects in CPS models due to the complexities involved in the software and physical systems. To find defects in CPS models efficiently, robustness guided falsification of CPS is introduced. Existing methods use several optimization techniques to generate counterexamples, which falsify the given properties of a CPS. However those methods may require a large number of simulation runs to find the counterexample and are far from practical. In this work, we explore state-of-the-art Deep Reinforcement Learning (DRL) techniques to reduce the number of simulation runs required to find such counterexamples. We report our method and the preliminary evaluation results. As the complexity of cyber-physical systems increases, so does the number of ways an adversary can disrupt them. This necessitates automated anomaly detection methods to detect possible threats. In this paper, we extend our recent results in the field of inference via formal methods to develop an unsupervised learning algorithm. Our procedure constructs from data a signal temporal logic (STL) formula that describes normal system behavior. Trajectories that do not satisfy the learned formula are flagged as anomalous. STL can be used to formulate properties such as “If the train brakes within 500 m of the platform at a speed of 50 km hr, then it will stop in at least 30 s and at most 50 s.” STL gives a more human-readable representation of behavior than classifiers represented as surfaces in high-dimensional feature spaces. STL formulae can also be used for early detection via online monitoring and for anomaly mitigation via formal synthesis. We demonstrate the power of our method with a physical model of a train's brake system. To our knowledge, this paper is the first instance of formal methods being applied to anomaly detection. This paper examines techniques for finding falsifying trajectories of hybrid systems using an approach that we call trajectory splicing. Many formal verification techniques for hybrid systems, including flowpipe construction, can identify plausible abstract counterexamples for property violations. However, there is often a gap between the reported abstract counterexamples and the concrete system trajectories. Our approach starts with a candidate sequence of disconnected trajectory segments, each segment lying inside a discrete mode. However, such disconnected segments do not form concrete violations due to the gaps that exist between the ending state of one segment and the starting state of the subsequent segment. Therefore, trajectory splicing uses local optimization to minimize the gap between these segments, effectively splicing them together to form a concrete trajectory. We demonstrate the use of our approach for falsifying safety properties of hybrid systems using standard optimization techniques. As such, our approach is not restricted to linear systems. We compare our approach with other falsification approaches including uniform random sampling and a robustness guided falsification approach used in the tool S-Taliro. Our preliminary evaluation clearly shows the potential of our approach to search for candidate trajectory segments and use them to find concrete property violations.