The paper tackles learning structured linear dynamical systems when only a few observations are available at each time step. It proposes an estimator that minimizes a bias‑corrected, potentially non‑convex objective and derives non‑asymptotic error bounds that depend on the local complexity of the constraint set, the trajectory length, and the sub‑sampling probability. The authors also prove convergence of projected gradient descent and demonstrate the theory for three specific constraint sets, showing that accurate recovery of the transition matrix is achievable with much shorter trajectories and very low observation rates.
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:2609.06182v1 Announce Type: cross Abstract: In this paper, we develop and analyze techniques for recovering a linear image $Bx$ of an unknown signal $x$ from indirect noisy observation $\omega=...
arXiv:2605. 17189v2 Announce Type: replace-cross Abstract: Inductive matrix completion (IMC) is a variant of low-rank matrix completion that incorporates row and column side-information.
arXiv:2506. 01052v3 Announce Type: replace Abstract: We investigate the finite-time convergence properties of Temporal Difference (TD) learning with linear function approximation, a cornerstone of reinforcement learning.
The paper presents high‑probability generalization guarantees for Randomized Block Coordinate Descent (RBCD) when applied to nonconvex learning problems. It derives bounds on the gradients of both empirical and population risks under standard smoothness assumptions, and shows how polynomially decaying step sizes and early stopping can achieve optimal convergence rates for population gradients. In settings where the objective is gradient‑dominated, the authors provide functional suboptimality bounds that approach optimistic rates seen in convex or low‑noise scenarios, and they also establish dimension‑independent bounds for loss functions with a particular structure, extending applicability to high‑dimensional problems.
arXiv:2610. 12328v1 Announce Type: new Abstract: We consider stochastic nonsmooth nonconvex composite optimization, which includes several important problems such as constrained optimization and the regularized training of neural networks.
arXiv:2609. 20687v1 Announce Type: cross Abstract: We study first-order black-box convex optimization over an $\ell_p$-ball for objectives Lipschitz in the $\ell_q$-norm, solving in the affirmative the nonsmooth version of the COLT open question (Guz15b) on whether the geometry of a smaller feasible set ($p < q$) can improve convergence rates in convex optimization, and matching prior lower bounds up to logarithmic factors.
The paper introduces a Projected Riemannian Gradient Descent (RGD) algorithm for computing the Bures‑Wasserstein barycenter of positive definite matrices, achieving dimension‑independent linear convergence at unit step size. It resolves a previous dichotomy by showing that clipping eigenvalues to a fixed interval yields a closed‑form, non‑expansive projection in the BW metric, allowing the algorithm to match the empirical speed of unit‑step RGD while maintaining theoretical guarantees. The method also extends to the invariant matrix projection problem, providing a unified dimension‑independent analysis.
arXiv:2603.15576v2 Announce Type: replace-cross Abstract: This paper develops new variance-reduction techniques for the forward-reflected-backward splitting (FRBS) method to solve a class of possibly...
The paper introduces a contraction framework for stochastic operators that incorporates bootstrapping, where a variable is updated using a frozen copy as a target that is refreshed every $K$ steps. By modeling the sampled update as a stochastic operator, the authors derive a finite‑time bound for i.i.d. samples that applies to any target‑update period and does not require gradient structure or uniformly bounded sampling error. The framework shows that the iterates converge geometrically in root mean square to a ball around the fixed point, with the error floor scaling with the step size, and it generalizes existing deterministic and stochastic‑gradient bounds.
arXiv:2609. 03762v1 Announce Type: new Abstract: The computation of the Bures-Wasserstein (BW) barycenter of an ensemble of positive definite matrices arises throughout machine learning, optimal transport, and quantum information.
arXiv:2609. 29961v1 Announce Type: new Abstract: Many iterative algorithms rely on bootstrapping.