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arXiv · 2205.02577

Moment-based Invariants for Probabilistic Loops with Non-polynomial Assignments

Andrey Kofnov·Marcel Moosbrugger·Miroslav Stankovič·Ezio Bartocci·Efstathia Bura
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Abstract

We present a method to automatically approximate moment-based invariants of probabilistic programs with non-polynomial updates of continuous state variables to accommodate more complex dynamics. Our approach leverages polynomial chaos expansion to approximate non-linear functional updates as sums of orthogonal polynomials. We exploit this result to automatically estimate state-variable moments of all orders in Prob-solvable loops with non-polynomial updates. We showcase the accuracy of our estimation approach in several examples, such as the turning vehicle model and the Taylor rule in monetary policy.

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Andrey Kofnov, Marcel Moosbrugger, Miroslav Stankovič, Ezio Bartocci, Efstathia Bura. 2022-05-05. Moment-based Invariants for Probabilistic Loops with Non-polynomial Assignments. https://doi.org/10.1007/978-3-031-16336-4_1

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