arXiv:2608. 04471v1 Announce Type: cross Abstract: Time series in real-world applications are often generated by nonlinear dynamical systems, making accurate forecasting challenging.
arXiv:2607. 06935v1 Announce Type: cross Abstract: Reinforcement learning (RL) is increasingly grounded in tools from probability, optimization, and operator theory.
arXiv:2411. 01982v2 Announce Type: replace-cross Abstract: We study the problem of learning controlled stochastic differential equations (SDEs) \[ dX_t = b(t,X_t,u_t)\,dt + \sigma(t,X_t,u_t)\,dW_t, \] whose drift and diffusion depend nonlinearly on time, state, and control values.
arXiv:2603. 14762v3 Announce Type: replace-cross Abstract: We study supervisory switching control for partially-observed linear dynamical systems.
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:2607. 19628v1 Announce Type: new Abstract: In this work we investigate reinforcement learning (RL) as a framework for the robust control of parametrized dynamical systems in presence of measurements and model uncertainties.
The paper presents a finite‑sample learning‑to‑control framework for geometrically supervised latent models of nonlinear deterministic systems. It introduces an encoder‑only local–global metric hinge that ensures directional resolution and state discrimination, and proves that any approximate empirical minimizer is pointwise co‑Lipschitz and uniformly approximately semiconjugate to the true dynamics under regularity assumptions. The results provide explicit bounds on approximation, sampling, and optimization errors, and demonstrate through controlled experiments that restoring metric resolution improves control performance.
arXiv:2606. 23827v1 Announce Type: cross Abstract: A data-driven method is developed for approximating value functions in deterministic optimal control problems with nonlinear control-affine dynamics.
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:2405. 07312v5 Announce Type: replace-cross Abstract: This paper presents a novel Koopman composition operator representation framework for control systems in reproducing kernel Hilbert spaces (RKHSs) that is free of explicit dictionary or input parametrizations.
arXiv:2302.07477v4 Announce Type: replace Abstract: We study the optimal sample complexity of tabular reinforcement learning for infinite-horizon discounted Markov decision processes. The unrestricte...
arXiv:2604. 06039v2 Announce Type: replace-cross Abstract: Value iteration-type methods have been extensively studied for computing a nearly optimal value function in reinforcement learning (RL).