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Proving expected sensitivity of probabilistic programs with randomized variable-dependent termination time

Authors:

Krishnendu Chatterjee,

Ming XuAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 4, Issue POPL

Article No.: 25, Pages 1 - 30

https://doi.org/10.1145/3371093

Published: 20 December 2019 Publication History

Abstract

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 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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Chatterjee KGoharshady ENovotný PŽikelić Đ(2024)Equivalence and Similarity Refutation for Probabilistic ProgramsProceedings of the ACM on Programming Languages10.1145/36564628:PLDI(2098-2122)Online publication date: 20-Jun-2024
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Index Terms

Proving expected sensitivity of probabilistic programs with randomized variable-dependent termination time
1. Theory of computation
  1. Logic
    1. Automated reasoning
    2. Logic and verification
  2. Semantics and reasoning
    1. Program reasoning
      1. Program verification

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 4, Issue POPL

January 2020

1984 pages

EISSN:2475-1421

DOI:10.1145/3377388

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Copyright © 2019 Owner/Author.

This work is licensed under a Creative Commons Attribution International 4.0 License.

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Association for Computing Machinery

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Published: 20 December 2019

Published in PACMPL Volume 4, Issue POPL

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Chatterjee KGoharshady ENovotný PŽikelić Đ(2024)Equivalence and Similarity Refutation for Probabilistic ProgramsProceedings of the ACM on Programming Languages10.1145/36564628:PLDI(2098-2122)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656462
Wang PYang TFu HLi GOng C(2024)Static Posterior Inference of Bayesian Probabilistic Programming via Polynomial SolvingProceedings of the ACM on Programming Languages10.1145/36564328:PLDI(1361-1386)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656432
Chatterjee KGoharshady AMeggendorfer TŽikelić Đ(2024)Quantitative Bounds on Resource Usage of Probabilistic ProgramsProceedings of the ACM on Programming Languages10.1145/36498248:OOPSLA1(362-391)Online publication date: 29-Apr-2024
https://dl.acm.org/doi/10.1145/3649824
Pasechnyuk DPrazdnichnykh AEvtikhiev MBryksin TBavota GHao D(2023)Judging Adam: Studying the Performance of Optimization Methods on ML4SE TasksProceedings of the 45th International Conference on Software Engineering: New Ideas and Emerging Results10.1109/ICSE-NIER58687.2023.00027(117-122)Online publication date: 17-May-2023
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Moosbrugger MMüllner JKovács L(2023)Automated Sensitivity Analysis for Probabilistic LoopsiFM 202310.1007/978-3-031-47705-8_2(21-39)Online publication date: 6-Nov-2023
https://doi.org/10.1007/978-3-031-47705-8_2
Zhou ZHuang ZMisailovic S(2023)AquaSense: Automated Sensitivity Analysis of Probabilistic Programs via Quantized InferenceAutomated Technology for Verification and Analysis10.1007/978-3-031-45332-8_16(288-301)Online publication date: 19-Oct-2023
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Wang JSun YFu HChatterjee KGoharshady AFreund SYahav E(2021)Quantitative analysis of assertion violations in probabilistic programsProceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation10.1145/3453483.3454102(1171-1186)Online publication date: 19-Jun-2021
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