Singular perturbations in stochastic optimal control with unbounded data

2022/08/01 by Bardi, Martino, Kouhkouh, Hicham · 1 citation
#35B25 #49L25 #93C70 #93E20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2208.00655

Abstract

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.

Cited by

• Singular Perturbations of Hamilton-Jacobi Equations in the Wasserstein Space

Related

• Deep Relaxation of Controlled Stochastic Gradient Descent via Singular Perturbations
• Singular Limit of Two Scale Stochastic Optimal Control Problems in Infinite Dimensions by Vanishing Noise Regularization
• A Neural Network Approach for Stochastic Optimal Control
• Singular Perturbation in Multiscale Stochastic Control Problems with Domain Restriction in the Slow Variable
• Mean-Field Neural ODEs via Relaxed Optimal Control