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.
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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.
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:2604. 26993v2 Announce Type: replace-cross Abstract: We study gradient descent for rank-1 matrix factorization through a state-dependent Lyapunov perspective.
arXiv:2608. 12828v1 Announce Type: cross Abstract: Distribution steering seeks feedback laws that drive the state law of a dynamical system between prescribed initial and terminal distributions.
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.