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A. Kofnov, M. Moosbrugger, S. Stankovic, E. Bartocci, E. Bura:
"Moment-based Invariants for Probabilistic Loops with non-polynomial assignments";
accepted as talk for: Proc. of QEST 2022: the 19th International Conference on Quantitative Evaluation of SysTems, Warsaw, Poland; 2022-09-12 - 2022-09-16; in: "Proc. of QEST'22: the 19th International Conference on Quantitative Evaluation of SysTems", (2022).

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.