Keywords: Verified Learning, Neurosymbolic Programs, Safe Learning, Symbolic Execution
TL;DR: We present DSE, the first approach to worst-case-safe parameter learning for potentially non-differentiable neurosymbolic programs where we bridge symbolic execution and stochastic gradient estimator to learn the loss of safety properties.
Abstract: We study the problem of learning verifiably safe parameters for programs that use neural networks as well as symbolic, human-written code. Such neurosymbolic programs arise in many safety-critical domains. However, because they need not be differentiable, they cannot be learned using existing approaches to integrating learning and verification. Our method, Differentiable Symbolic Execution (DSE), learns such programs by sampling code paths using symbolic execution, constructing gradients of a worst-case ``safety loss'' along these paths, and then backpropagating these gradients through program operations using a generalization of the reinforce estimator. We evaluate the method on a mix of synthetic tasks and real-world control and navigation benchmarks. Our experiments show that DSE significantly outperforms the state-of-the-art DiffAI method on these tasks.
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