The paper presents time‑uniform self‑normalized concentration bounds for stochastic processes in Hilbert spaces with vector‑valued noise, enabling regression‑error guarantees for both linear and nonlinear parametric operators. These results apply to possibly infinite‑dimensional inputs and outputs without requiring independence or mixing assumptions, and are derived in the context of sequentially collected, dependent data such as adaptive experimental design and dynamical‑system modelling.
arXiv:2402.04691v5 Announce Type: replace-cross Abstract: This study investigates the use of stochastic gradient descent (SGD) to learn operators between general Hilbert spaces. We study weak and str...
arXiv:2504.18184v5 Announce Type: replace Abstract: We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert sp...
The paper presents a fully data-driven method for optimal control of nonlinear control‑affine systems modeled as stochastic diffusions. It embeds state probability densities into a reproducing kernel Hilbert space to learn Markov transition operators, which are then used in convex operator‑theoretic Hamilton‑Jacobi‑Bellman recursions that scale linearly with state dimensionality. Numerical experiments show the approach can solve diverse nonlinear control tasks, such as depth regulation of an autonomous underwater vehicle.
arXiv:2607. 22399v1 Announce Type: cross Abstract: We consider the problem of learning from a single finite trajectory of an ergodic stochastic dynamical system.
The paper introduces an operator-theoretic approach to offline reinforcement learning for continuous-time stochastic systems. By linking reinforcement learning to the Hamilton‑Jacobi‑Bellman equation, it proposes a dynamic programming recursion that represents the world model through the infinitesimal generator of controlled diffusion processes learned in a reproducing kernel Hilbert space. The authors establish global convergence of the value function under small generator‑approximation error and provide explicit finite‑sample guarantees tied to system properties such as smoothness and stability.
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.
We develop a comprehensive theory for regularized M-estimation in reproducing kernel Hilbert spaces. Under mild conditions on the loss we establish existence and measurability of the estimator, covering a wide range of convex and non-convex losses, including bounded robust losses.
arXiv:2610.19391v1 Announce Type: new Abstract: We study continuous global optimization problems in which the objective function cannot be directly evaluated; rather, we observe only which of two sel...
arXiv:2603. 16481v3 Announce Type: replace Abstract: Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data, and thus, a key enabler for safe learning-based control.
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:2312. 15341v1 Announce Type: cross Abstract: We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems.
arXiv:2606. 30230v1 Announce Type: cross Abstract: Learned reconstruction operators for inverse problems are typically trained under a fixed noise model, and generalize poorly when the distribution during testing differs from the one assumed during training.