Singular perturbations in stochastic optimal control with unbounded data

Martino Bardi; Hicham Kouhkouh

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arXiv · 2208.00655

Singular perturbations in stochastic optimal control with unbounded data

Martino Bardi·Hicham Kouhkouh

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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.

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Martino Bardi, Hicham Kouhkouh. 2022-08-01. Singular perturbations in stochastic optimal control with unbounded data. https://arxiv.org/abs/2208.00655

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