arXiv:2610. 11906v1 Announce Type: cross Abstract: We consider the problem of learning linear dynamical systems under adversarial contamination from a single trajectory of length $T$.
arXiv:2606. 27685v1 Announce Type: cross Abstract: Pervasive data contamination -- stemming from measurement errors, outliers, or adversarial corruption -- has motivated the development of robust statistical methods.
arXiv:2410. 07719v4 Announce Type: replace Abstract: Despite being widely adopted as a canonical framework for learning robust models, adversarial training suffers from robust overfitting.
arXiv:2603.01337v2 Announce Type: replace Abstract: We study adaptive estimation and inference in linear inverse problems defined by conditional moment restrictions. These problems are typically ill-...
arXiv:2609. 39449v1 Announce Type: new Abstract: Distributionally robust optimization (DRO) studies parameter estimation under uncertainty in the underlying probability distribution and has emerged as a principled framework for analyzing robustness and generalization.
The paper revisits median‑of‑means estimation from a deterministic optimization perspective, introducing a family of block‑Lp estimators (for 0 < p ≤ 1) that achieve robust learning with heavy‑tailed and adversarially corrupted data. It shows that any convex block M‑estimator cannot attain the trimmed‑block oracle constant, while the nonconvex block‑Lp family provides finite‑sample robustness bounds that approach this oracle constant as p decreases. The authors also prove that the block‑Lp objectives have a benign landscape—every local minimum is close to the true parameter—and combine these results with block‑level concentration to obtain sub‑Gaussian deviation bounds under finite 2+δ moments, extending to high‑dimensional robust mean estimation and sparse regression.
arXiv:2605. 29497v2 Announce Type: replace Abstract: We study the problem of robustly learning Gaussian Single Index Models (SIMs) in the presence of heavy-tailed noise and a constant fraction of adversarially corrupted covariates and responses.
The paper investigates how the choice of the π parameter in λπ norm-constrained adversarial attacks influences the sparsity and smoothness of the perturbations. By applying two established sparsity metrics and introducing three new smoothness measures—including one based on first-order Taylor approximations—the authors perform extensive experiments on real-world image datasets and various neural network architectures. Their results indicate that λρ norms with π values between 1.3 and 1.5 consistently provide the best balance between sparsity and smoothness, challenging the common use of λ1 or λ2 norms.
The paper studies federated learning where honest clients have heterogeneous data-generating models and adversarial clients can exacerbate this heterogeneity by sending arbitrary updates. It derives new bounds on gradient heterogeneity for linear and nonlinear regression, separating effects from honest clients’ model differences, label noise, and initialization. The authors show that for any (f,κ)-robust aggregator with κ = O(f/n) (where f is the number of adversarial clients and n the total number of clients, with f/n < 1/2), convergence is guaranteed after an explicit sample burn‑in period.
arXiv:2509. 19242v2 Announce Type: replace-cross Abstract: We study multivariate linear regression under Gaussian covariates in two settings, where data may be erased or corrupted by an adversary under a coordinate-wise budget.
arXiv:2606. 19652v1 Announce Type: new Abstract: In this work, we introduce a training procedure for shallow neural networks that promotes robustness against adversarial attacks.
arXiv:2506.12454v2 Announce Type: replace-cross Abstract: What fundamentally distinguishes an adversarial attack from a misclassification due to limited model expressivity or finite data? In this wor...
arXiv:2607. 03839v1 Announce Type: new Abstract: Sparse feature selection is critical for high-dimensional machine learning, yet traditional $\ell_1$-regularized methods are often brittle under observational noise and spurious correlations, leading to unstable feature supports and degraded generalization.