一句话：提出基于鞅的可靠方法，证明迭代次数随机依赖输入的概率 while 循环的期望敏感性，并可自动化与组合。
本文研究概率程序的期望敏感性（expected sensitivity），即程序输入的变化会导致输出成比例变化。已有工作仅能处理迭代次数固定且有界的概率 while 循环。本文针对迭代次数随机且依赖于初始输入值的概率 while 循环，提出一种可靠的证明方法。该方法基于鞅（martingale）理论，可利用现有鞅合成算法实现自动化；在温和的边条件下，方法对 while 循环的顺序组合具有组合性。作者在赌徒破产、随机混合系统和随机梯度下降等经典例子上展示了方法有效性，并给出实验结果，表明自动化方法能处理文献中的多种概率程序。
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.
@article{paperbot566,
title = {Proving expected sensitivity of probabilistic programs with randomized variable-dependent termination time},
author = {Peixin Wang and Hongfei Fu and Krishnendu Chatterjee and Yuxin Deng and Ming Xu},
journal = {Proceedings of the ACM on Programming Languages},
volume = {4},
number = {POPL},
year = {2019},
doi = {10.1145/3371093}
}