Robust methods improve learning linear systems with bad data
RobustLDS: Learning linear dynamical systems under adversarial corruptions
Machine Learning
Summary
Learning how systems change over time is common in science and engineering, but sometimes the observations or data collected can be wrong or tricky on purpose. This paper looks at how to learn the rules of such systems even when some of the data points are deliberately corrupted or misleading. The authors propose new methods that can handle these bad data points and still figure out the system accurately. They also test their methods and show they work well in practice.
What this means in practice
- •For control system engineers: Enhance system models by accurately identifying dynamics despite corrupted sensor data in critical industrial controls.
- •For data engineers in robotics: Improve robot state tracking by filtering out adversarial or faulty observations during model learning from movement data.
Authors
Aravinda Kanchana Ruwanpathirana, Hemant Tyagi
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.