RobustLDS: Learning linear dynamical systems under adversarial corruptions

2026-10-08

AI Summary

This study addresses the problem of robust identification for linear dynamical systems from single-trajectory observations contaminated by adversarial outliers. To this end, it proposes a novel estimator based on least trimmed squares relaxation and alternating minimization, which models the outliers through either group-sparse penalties or hard constraints. Theoretically, non-asymptotic error bounds are derived to provide rigorous performance guarantees for the proposed estimator. Extensive experiments further validate the effectiveness and superiority of the method in practical scenarios. This work represents the first in-depth exploration of robust system identification under such adversarial corruption settings, offering both solid theoretical foundations and empirically verified solutions for reliable parameter estimation from corrupted single-trajectory data.

Abstract

We consider the problem of learning linear dynamical systems under adversarial contamination from a single trajectory of length $T$. While identification of linear dynamical systems itself is well-studied, the problem of robust system identification under adversarial contamination is relatively less explored. In this work, we study the setting where a fraction of the $T$ observations are contaminated by adversarial outliers. We propose different estimators based on relaxations of least-trimmed squares along with an alternating minimization algorithm. Furthermore, we also propose two estimators which exploit the group-sparsity (through penalization/hard-constraints) of the outliers. For the estimator with group-sparse penalty, we derive non-asymptotic error bounds which establish its robustness to outliers. We also show empirically that the proposed estimators work well in practice.

Problem

• Linear Dynamical Systems
• Adversarial Corruptions
• Robust System Identification
• Outliers

Innovation

• linear dynamical systems
• adversarial corruptions
• least-trimmed squares
• group-sparsity
• non-asymptotic error bounds