Reinforcement learning is a promising approach to solving hard robotics tasks. An important challenge is ensuring safety-e.g., that a walking robot does not fall over or an autonomous car does not crash into an obstacle. We build on an approach that composes the learned policy with a backup policy-it uses the learned policy on the interior of the region where the backup policy is guaranteed to be safe, and switches to the backup policy on the boundary of this region. The key challenge is checking when the backup policy is guaranteed to be safe. Our algorithm, statistical model predictive shielding (SMPS), uses sampling-based verification and linear systems analysis to perform this check. We prove that SMPS ensures safety with high probability, and empirically evaluate its performance on several benchmarks.
We present counterfactual symbolic execution, a new approach that produces counterexamples that localize the causes of failure of static verification. First, we develop a notion of symbolic weak head normal form and use it to define lazy symbolic execution reduction rules for non-strict languages like Haskell. Second, we introduce counterfactual branching, a new method to identify places where verification fails due to imprecise specifications (as opposed to incorrect code). Third, we show how to use counterfactual symbolic execution to localize refinement type errors, by translating refinement types into assertions. We implement our approach in a new Haskell symbolic execution engine, G2, and evaluate it on a corpus of 7550 errors gathered from users of the LiquidHaskell refinement type system. We show that for 97.7% of these errors, G2 is able to quickly find counterexamples that show how the code or specifications must be fixed to enable verification. CCS Concepts • Theory of computation → Abstraction; • Computing methodologies → Symbolic and algebraic manipulation.
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