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.
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.
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.
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:2607. 22982v1 Announce Type: new Abstract: Natural Policy Gradient (NPG) is a well-established Reinforcement Learning algorithm that underlies widely used methods such as Trust Region Policy Optimization and Proximal Policy Optimization, both of which have demonstrated strong empirical success.
arXiv:2608. 13651v1 Announce Type: cross Abstract: We solve exactly a fundamental problem of adaptive control against adversarial disturbances: regulate the scalar system $x_{t+1} = ax_t + u_t + w_t$, $x_0=0$, $\|w\|_\infty \le 1$, where the constant pole $a \in [-\Delta, \Delta]$ is unknown in sign and magnitude and $\Delta$ is arbitrarily large.
arXiv:2607. 03639v1 Announce Type: cross Abstract: For a multidimensional reflected diffusion, determining whether the associated basic adjoint relationship (BAR) uniquely characterizes the stationary distribution is a basic uniqueness problem in the BAR approach.
arXiv:2609.06467v1 Announce Type: new Abstract: In performative reinforcement learning the deployed policy shapes the environment that generates the learner's future data, and the natural solution co...
arXiv:2608. 26515v1 Announce Type: cross Abstract: We study online prediction for a specific finite-alphabet, exogenously driven source with infinite input memory.
arXiv:2608. 15337v1 Announce Type: cross Abstract: We disprove the expectation stated by Xin, Yu, and Ronney that the physical positive part strain $G$-equation should possess an effective burning velocity in cellular flows.
arXiv:2609. 21880v1 Announce Type: cross Abstract: We study the optimization of convex objectives with $(L,\kappa-1)$-H\"older-continuous gradients in $\ell_q$ over $R B_p^d$, $1<\kappa\le 2$.
arXiv:2607. 16384v1 Announce Type: new Abstract: For stochastic gradient descent (SGD) with a constant stepsize $\alpha$, the invariant law of the iterates, centered at a minimizer, describes the behavior of the algorithm over long time horizons.
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...