Ever since the concepts of dynamic programming were introduced, one of the
most difficult challenges has been to adequately address high-dimensional
control problems. With growing dimensionality, the utilisation of Deep Neural
Networks promises to circumvent the issue of an otherwise exponentially
increasing complexity. The paper specifically investigates the sampling issues
the Deep Galerkin Method is subjected to. It proposes a drift relaxation-based
sampling approach to alleviate the symptoms of high-variance policy
approximations. This is validated on mean-field control problems; namely, the
variations of the opinion dynamics presented by the Sznajd and the
Hegselmann-Krause model. The resulting policies induce a significant cost
reduction over manually optimised control functions and show improvements on
the Linear-Quadratic Regulator problem over the Deep FBSDE approach.

通过采用基于漂移放松的采样方法，本文研究了 Deep Galerkin 方法所面临的采样问题，通过验证 Sznajd 和 Hegselmann-Krause 模型中的意见动态变化的多场控制问题，得出的策略在手动优化控制函数上实现了显著成本降低，并在 Deep FBSDE 方法上改进了线性 - 二次调节器问题。