# RobustLDS: Learning linear dynamical systems under adversarial corruptions

arXiv: https://arxiv.org/abs/2610.11906 · HTML: https://mlsanity.com/paper/2610.11906/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 76 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 10 of 10)

- [Optimal Robust Linear Regression in Nearly Linear Time](https://mlsanity.com/paper/2007.08137/) (2020)
- [Robust and Sparse Estimation of Linear Regression Coefficients with Heavy-tailed Noises and Covariates](https://mlsanity.com/paper/2206.07594/) (2022)
- [Learning linear dynamical systems under convex constraints](https://mlsanity.com/paper/2303.15121/) (2023)
- [Robust estimation with Lasso when outputs are adversarially contaminated](https://mlsanity.com/paper/2004.05990/) (2020)
- [High Dimensional Robust M-Estimation: Arbitrary Corruption and Heavy Tails](https://mlsanity.com/paper/1901.08237/) (2019)
- [Robust Sparse Estimation for Gaussians with Optimal Error under Huber Contamination](https://mlsanity.com/paper/2403.10416/) (2024)
- [Efficient and Consistent Robust Time Series Analysis](https://mlsanity.com/paper/1607.00146/) (2016)
- [Tail-robust estimation of factor-adjusted vector autoregressive models for high-dimensional time series](https://mlsanity.com/paper/2509.22235/) (2025)
- [System Identification under Noise and Attack Regimes: Agnostic and Composite Robustness](https://mlsanity.com/paper/2602.07288/) (2026)
- [Huber-based Robust System Identification with Near-Optimal Guarantees Across Independent and Adversarial Regimes](https://mlsanity.com/paper/2603.27586/) (2026)

## Abstract (arXiv)

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.