Proving Expected Sensitivity of Probabilistic Programs with Randomized Variable-Dependent Termination Time
The notion of program sensitivity (aka Lipschitz continuity) specifies that changes in the program input result in proportional changes to the program output. For probabilistic programs the notion is naturally extended to expected sensitivity. A previous approach develops a nice relational program logic framework for proving expected sensitivity of probabilistic while loops, where the number of iterations is fixed and bounded. In this work, we consider probabilistic while loops where the number of iterations is not fixed, but randomized and depends on the initial input values. We present a sound approach for proving expected sensitivity of such programs. Our sound approach is martingale-based and can be automated through existing martingale-synthesis algorithms. Furthermore, our approach is compositional for sequential composition of while loops under a mild side condition. We demonstrate the effectiveness of our approach on several classical examples from Gambler’s Ruin, stochastic hybrid systems and stochastic gradient descent. We also present experimental results showing that our automated approach can handle various probabilistic programs in the literature.
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|Proving Expected Sensitivity of Probabilistic Programs with Randomized Variable-Dependent Termination Time|
Peixin WangShanghai Jiao Tong University, Hongfei FuShanghai Jiao Tong University, Krishnendu ChatterjeeIST Austria, Yuxin DengEast China Normal University, Ming XuEast China Normal UniversityLink to publication DOI Media Attached
|Aiming Low Is Harder: Induction for Lower Bounds in Probabilistic Program Verification|
Marcel HarkRWTH Aachen University, Germany, Benjamin Lucien KaminskiRWTH Aachen University, Germany, Jürgen GieslRWTH Aachen University, Joost-Pieter KatoenRWTH Aachen UniversityLink to publication DOI Media Attached File Attached