# Temporal Robustness in Discrete Time Linear Dynamical Systems

arXiv: https://arxiv.org/abs/2505.02347 · HTML: https://mlsanity.com/paper/2505.02347/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 54 references that are in the map.
- First posted on arXiv 5 May 2025.

## Builds on (most cited first, 19 of 19)

- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Variance-based regularization with convex objectives](https://mlsanity.com/paper/1610.02581/) (2016)
- [Near optimal finite time identification of arbitrary linear dynamical systems](https://mlsanity.com/paper/1812.01251/) (2018)
- [Distributionally Robust Optimization: A Review](https://mlsanity.com/paper/1908.05659/) (2019)
- [The Curious Price of Distributional Robustness in Reinforcement Learning with a Generative Model](https://mlsanity.com/paper/2305.16589/) (2023)
- [Spectral Filtering for General Linear Dynamical Systems](https://mlsanity.com/paper/1802.03981/) (2018)
- [New Bounds for Matrix Multiplication: from Alpha to Omega](https://mlsanity.com/paper/2307.07970/) (2023)
- [Explicit Tradeoffs between Adversarial and Natural Distributional Robustness](https://mlsanity.com/paper/2209.07592/) (2022)
- [Wasserstein distributional robustness of neural networks](https://mlsanity.com/paper/2306.09844/) (2023)
- [Distributionally Robust Constrained Reinforcement Learning under Strong Duality](https://mlsanity.com/paper/2406.15788/) (2024)
- [On Learning Markov Chains](https://mlsanity.com/paper/1810.11754/) (2018)
- [Distributionally Robust Submodular Maximization](https://mlsanity.com/paper/1802.05249/) (2018)
- [Tensor Decompositions Meet Control Theory: Learning General Mixtures of Linear Dynamical Systems](https://mlsanity.com/paper/2307.06538/) (2023)
- [Learning linear dynamical systems under convex constraints](https://mlsanity.com/paper/2303.15121/) (2023)
- [Wasserstein Distance to Independence Models](https://mlsanity.com/paper/2003.06725/) (2020)
- [Optimal Transport to a Variety](https://mlsanity.com/paper/1909.11716/) (2019)
- [Scalable Distributional Robustness in a Class of Non Convex Optimization with Guarantees](https://mlsanity.com/paper/2205.15624/) (2022)

## Abstract (arXiv)

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.