Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.10029

A Nonlocal Stochastic Optimal Control with Elliptic-Type Smoothing

Stefana-Lucia Anita·Luca Di Persio
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study a nonlocal stochastic optimal control problem in which the control acts through the elliptic smoothing operator $\mathcal{S}=(I-Δ)^{-1}$ on $\mathbb{R}^d$. The state is described by the law of a controlled diffusion, equivalently by a controlled Fokker-Planck equation with coefficients depending on $\mathcal{S}u$. We prove the existence of an optimal control by the direct method in the calculus of variations. We then derive a Pontryagin-type maximum principle by spike variations, relying on sharp properties of the operator $\mathcal{S}$. The result yields a pointwise minimisation rule for the optimal control. We discuss the meaning of the optimal control problem in the case of population dynamics.

Explore related subjects

math.OC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Stefana-Lucia Anita, Luca Di Persio. 2026-10-07. A Nonlocal Stochastic Optimal Control with Elliptic-Type Smoothing. https://arxiv.org/abs/2610.10029

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Perturbed Iterate SGD for Lipschitz Continuous Loss Functions with Numerical Error and Adaptive Step Sizes

Motivated by neural network training in finite-precision arithmetic environments, this work studies the convergence of perturbed iterate SGD using adaptive step sizes in an environment with numerical error. Considering a general stochastic Lipschitz continuous loss function, an asymptotic convergence result to a Clarke stationary point is proven as well as the non-asymptotic convergence to an approximate stationary point in expectation. It is assumed that only an approximation of the loss function's stochastic gradient can be computed, in addition to error in computing the SGD step itself.

math.OC↗
arXiv2026

Sharp bounds in perturbed smooth optimization

This paper studies the problem of perturbed convex and smooth optimization. The main results describe how the solution and the value of the problem change if the objective function is perturbed. Examples include linear, quadratic, and smooth additive perturbations. Such problems naturally arise in statistics and machine learning, stochastic optimization, stability and robustness analysis, inverse problems, optimal control, etc. The results provide accurate expansions for the difference between the solution of the original problem and its perturbed counterpart with an explicit error term.

math.OC↗
arXiv2026

Controllability Allocation Scores for Targeted Network Intervention

We introduce the controllability allocation score (CAS), a framework for determining how intervention intensity should be distributed among prescribed candidate input directions with respect to designated target variables, together with the target controllability score (TCS) as its nodewise specialization. We establish existence of the CASs and develop a general uniqueness theory based on restricted injectivity of the allocation-to-Gramian map, including generic uniqueness with respect to the time horizon. We show that restricting attention to target variables can fundamentally alter the optimal intervention allocation compared with the standard full-state setting. To enable scalability, we develop a general surrogate-Gramian framework and derive objective-performance guarantees from relative Gramian errors without requiring uniqueness or closeness of the CASs. For the TCS specialization, we further construct a target-only reduced virtual system and derive explicit bounds showing how the approximation error depends on the coupling between target and non-target nodes and on the dynamical growth rate. Experiments on human brain networks show that the reduced formulation accurately approximates the TCS at short horizons, whereas the two controllability criteria exhibit markedly different approximation accuracy at long horizons.

math.OC↗