arXiv:2606. 17762v2 Announce Type: replace-cross Abstract: Finite-horizon optimal-control computations repeatedly solve two-point Pontryagin boundary value problems whose conditioning can deteriorate as the horizon grows.
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arXiv:2606. 17762v1 Announce Type: cross Abstract: We study horizon-uniform local branches of finite-horizon discrete-time Pontryagin boundary value systems after smooth control elimination.
The paper investigates local stationary solutions of finite‑horizon discrete‑time Pontryagin systems near a steady extremal. Under regularity of the stationarity equation, hyperbolicity of the reduced state–costate map, and a scaled transversality condition, the linearized boundary‑value problem admits a uniformly bounded inverse, leading to existence, uniqueness, and uniform Lipschitz estimates independent of the horizon. The study further shows that perturbations of the terminal reward decay exponentially with the horizon, and for linear‑quadratic systems with suitable conditions the Riccati matrix and initial feedback gain converge at a quantified rate, with numerical experiments confirming the theoretical predictions.
The paper proposes a new receding‑horizon algorithm for the Linear Quadratic Regulator (LQR) with unknown dynamics, inspired by REINFORCE. It removes the need for two‑point gradient estimates and does not require a stable initial policy, while maintaining the same order of sample complexity. A refined analysis of error propagation via the Riccati operator’s contraction under Riemannian distance yields improved sample complexity and convergence guarantees.
arXiv:2607. 23642v1 Announce Type: cross Abstract: Discrete optimization algorithms are often analyzed through continuous-time limiting ODEs, but a convergence certificate for the ODE is not automatically one for the discrete algorithm.
arXiv:2406. 07746v4 Announce Type: replace-cross Abstract: We propose a computationally efficient algorithm that achieves anytime regret of order $\mathcal{O}(\sqrt{t})$, with explicit dependence on the system dimensions and on the solution of the Discrete Algebraic Riccati Equation (DARE).
arXiv:2606. 09047v1 Announce Type: cross Abstract: A classical universal stabilization formula offers the practitioner no design freedom: it is a single, parameter-free object.