The paper introduces an active learning algorithm for linear system identification that uses optimal centered noise excitation. It employs ordinary least squares and semidefinite programming to achieve minimal sample complexity while enabling efficient computation of the system matrix estimate. The authors provide both lower and upper bounds on sample complexity that match up to universal factors and explicitly depend on system parameters such as state dimension.
arXiv:2606. 14095v1 Announce Type: new Abstract: We study the sample complexity of learning in average-reward weakly-coupled Markov decision processes (WCMDPs) and Restless Bandits (RBs) under a generative model.
arXiv:2609.08740v1 Announce Type: new Abstract: In this paper we derive a Probably Approximately Correct (PAC)-Bayesian error bound for partially observed linear time-invariant (LTI) stochastic dynam...
arXiv:2512. 05337v2 Announce Type: replace-cross Abstract: We consider the problem of learning the parameters of a $N$-dimensional stochastic linear dynamics under both full and partial observations from a single trajectory of time $T$.
arXiv:2606. 12182v1 Announce Type: new Abstract: Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering.
This paper studies active regression for single-index models under general $\ell_p$-loss with an unknown $1$-Lipschitz link function $f$, formulated as $\min_{f,x} \|f(Ax)-b\|_p^p$ with full access to $A$ but coordinate-query access to $b$. Prior work established upper bounds for known link functions for all $p\geq 1$ and for unknown link functions only in the $p=2$ case, together with lower bounds for $p\leq 2$.
arXiv:1711. 10051v4 Announce Type: replace Abstract: We present an approach that improves the sample complexity for a variety of curve fitting problems, including active learning for linear regression, polynomial regression, and continuous sparse Fourier transforms.
Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering. While early approaches relied on empirical data and heuristics, modern data-driven methods offer greater flexibility and fewer assumptions.
The paper introduces a structured method for learning linear operators in control systems using data. It leverages the framework of (semi)groups for evolution equations to establish structural assumptions and applies inverse‑problems theory to analyze learning algorithms, revealing error decompositions, convergence guarantees, and optimal regularization. Focusing on bounded operators on Hilbert spaces, the authors derive a convergent estimator for time‑varying systems, illustrating the practical power of their approach.
arXiv:2609.09211v1 Announce Type: new Abstract: The Davis-Kahan theorem is a fundamental tool in spectral analysis, providing quantitative control over the distance between the eigenspaces of a symme...
arXiv:2608. 12503v1 Announce Type: cross Abstract: We describe a simple rejection-sampling-based algorithm to perform length-squared sampling on an $n \times n$ positive-semidefinite (psd) matrix: that is, to sample a column with probability proportional to its squared $\ell_2$-norm.
arXiv:2608.30431v1 Announce Type: cross Abstract: By focusing on algorithmic stability as a means of establishing out-of-sample bounds, we provide a system-theoretic interpretation of generalization...
arXiv:2505. 12037v2 Announce Type: replace Abstract: Learning the optimal policy for Markov decision process problems (MDPs) from samples is a fundamental problem in online and data-driven decision-making.