论文标题
随机最佳控制中的奇异扰动和无界数据
Singular perturbations in stochastic optimal control with unbounded data
论文作者
论文摘要
我们研究具有无限数据的一类二级随机控制系统的奇异扰动。这些假设旨在涵盖深层神经网络的一些放松问题。我们构建有效的哈密顿量和初始数据，并证明了对HJB类型的抛物线方程的限制（有效）问题的解决方案（有效）问题的融合。我们使用概率，粘度解决方案和均质化方法。
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.
