Singular perturbations in stochastic optimal control with unbounded data

被引：3

作者：

Bardi, Martino ^{[1
]}

Kouhkouh, Hicham ^{[2
]}

机构：

[1] Univ Padua, Dept Math T Levi Civita, Via Trieste 63, I-35121 Padua, Italy

[2] Rhein Westfal TH Aachen, Inst Math, RTG Energy Entropy & Dissipat Dynam, Templergraben 55 111810, D-52062 Aachen, Germany

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2023年 / 29卷

关键词：

Singular perturbations; two-scale systems; stochastic optimal control; homogenization; viscosity solutions; Hamilton-Jacobi-Bellman equations; invariant measures; DIFFUSION-APPROXIMATION; POISSON-EQUATION; VISCOSITY SOLUTIONS; LARGE DEVIATIONS; CONVERGENCE;

D O I：

10.1051/cocv/2023020

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We study singular perturbations of a class of two-scale stochastic control systems with unbounded data. The assumptions are designed to cover some relaxation problems for deep neural networks. We construct effective Hamiltonian and initial data and prove the convergence of the value function to the solution of a limit (effective) Cauchy problem for a parabolic equation of HJB type. We use methods of probability, viscosity solutions and homogenization.

引用

页数：25

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