Defense Filters for Robust Learning of Partially Observed Dynamical Systems
Abstract
Robust estimation of unknown system dynamics from partial observations under attack is a core challenge in learning for control, increasingly critical in multi-agent networks subject to adversarial data poisoning. Existing methods either require highly restrictive assumptions on the adversary or yield weak error bounds. In this paper, we consider identifying partially observed linear dynamical systems subject to adversarial attacks with an attack probability p < 0.5 at each time. We propose a defense-filtering framework in which a system designer leverages knowledge of the observation matrix to construct a defense filter satisfying full column rank and subspace separability conditions, which enables the evaluation of a single-attack scenario against observed data. Using this framework, we analyze the constrained ℓ2-norm estimator and establish finite-sample error bounds for recovering the Markov parameter matrix G*. This is the first approach to provide provable system identification guarantees via a defense filter for partially observed systems subject to harsh attack environments where the attack probability approaches $0.5$.
Related
- Causal Fingerprints Reveal Hidden Mechanisms in Partially-Observed Dynamical Systems
- PAC-Bayesian Bounds for Learning Partially Observed Stochastic Linear Time-Invariant State-Space Systems with Inputs and Sub-Gaussian Noise
- Partially Observed McKean--Vlasov Control with Vanishing Observation Intensities
- A Stochastic Maximum Principle for Partially Observed Jump-Diffusion Systems with State-Dependent Counting-Process Observations
- Robust Covariance Estimation for Entry-wise Contaminated and Partially Observed Data via Expectation Maximization Algorithm
BibTeX
@misc{kim2026defense,
title = {{Defense Filters for Robust Learning of Partially Observed Dynamical Systems}},
author = {Jihun Kim and Javad Lavaei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21935},
eprint = {2610.21935},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21935},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Defense Filters for Robust Learning of Partially Observed Dynamical Systems
AU - Jihun Kim
AU - Javad Lavaei
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21935
UR - https://arxiv.org/abs/2610.21935
AB - Robust estimation of unknown system dynamics from partial observations under attack is a core challenge in learning for control, increasingly critical in multi-agent networks subject to adversarial data poisoning. Existing methods either require highly restrictive assumptions on the adversary or yield weak error bounds. In this paper, we consider identifying partially observed linear dynamical systems subject to adversarial attacks with an attack probability p < 0.5 at each time. We propose a defense-filtering framework in which a system designer leverages knowledge of the observation matrix to construct a defense filter satisfying full column rank and subspace separability conditions, which enables the evaluation of a single-attack scenario against observed data. Using this framework, we analyze the constrained ℓ_2-norm estimator and establish finite-sample error bounds for recovering the Markov parameter matrix G^*. This is the first approach to provide provable system identification guarantees via a defense filter for partially observed systems subject to harsh attack environments where the attack probability approaches $0.5$.
ER -