arXiv:2607. 07204v2 Announce Type: replace-cross Abstract: Structured preconditioners restrict optimization to a small family of positive metrics, but endpoint condition-number reachability does not measure the geometric effort required to reach a useful metric.
By Zavier Li
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.
By Pyuyi Chufeng Huang, Zikang Song
arXiv:2605. 07116v2 Announce Type: replace Abstract: We analyze a neural semi-discrete method for high-dimensional first-order Hamilton-Jacobi-Bellman (HJB) equations with known or learned dynamics.
By Minseok Kim, Yeongjong Kim, Namkyeong Cho, Yeoneung Kim
arXiv:2607. 13943v1 Announce Type: cross Abstract: Inspired by interior-point methods (IPM) for structured convex optimization, Kannan and Narayanan introduced the Dikin walk for sampling uniformly from polytopes in 2009.
By Yunbum Kook
While entropy regularization is widely used to stabilize and accelerate Natural Policy Gradient methods, its ability to yield faster convergence rates for the unregularized objective remains underexplored. Existing analyses often rely on double-loop architectures and invoke a linear entropy penalty.
arXiv:2607. 03503v1 Announce Type: new Abstract: Graph-based semi-supervised learning (SSL) propagates a few labels over a similarity graph by minimizing a Dirichlet-type energy.
By Oren E. Livne