研究离散时间线性系统在不确定时长下的鲁棒成本估算，提升安全与健康场景决策可靠性。
Temporal Robustness in Discrete Time Linear Dynamical Systems
- 将系统停止时的成本建模为瓦瑟斯坦模糊集下的分布鲁棒优化问题
- 证明马尔可夫链与全局渐近稳定系统的等价性，简化分析框架
- 提出多项式时间算法并验证在真实安全与医疗数据中的有效性
离散时间线性动态系统（包括马尔可夫链）已广泛应用于网络安全运营中心（CSOC）管理和健康风险控制等场景。然而，在这些应用中，系统运行时长存在不确定性，导致系统终止时的状态分布及其对应的成本（或收益）难以预估。基于历史运行时长样本，本文将停止时刻的成本估计问题形式化为瓦瑟斯坦模糊集下的分布鲁棒优化任务。为此，我们证明了定义在概率单纯形上的离散时间马尔可夫链与全局渐近稳定（GAS）离散时间线性系统之间的等价性，从而可仅基于GAS系统进行研究。进一步地，我们针对不同情形给出了多项式时间算法及复杂性下界，并提供了关于瓦瑟斯坦距离相关多面体的一个新证明。最后，我们在真实的CSOC数据和已有健康领域数据上进行了实验，验证了所提方法的有效性与优势。
原文摘要 · Abstract (English)
Discrete time linear dynamical systems, including Markov chains, have found many applications including in security settings such as in cybersecurity operations center (CSOC) management and in managing health risks. However, in these two scenarios, there is uncertainty about the time horizon for which the system runs. This creates uncertainty about the cost (or reward) incurred based on the state distribution when the system stops. Given past data samples of how long a system ran, we theoretically analyze the cost incurred at the stop of the system as a distributional robust cost estimation task in a Wasserstein ambiguity set. Towards this, we show an equivalence between a discrete time Markov Chain on a probability simplex and a global asymptotic stable (GAS) discrete time linear dynamical system, allowing us to base our study on a GAS system only. Then, we provide various polynomial time algorithms and hardness results for different cases in our theoretical study, including a novel proof of a fundamental result about Wassertein distance based polytope. We experiment with real world data in CSOC domain and prior data in health domain to reveal the benefits of our model and approach.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。