We propose a novel framework for solving continuous-time non-Markovian
stochastic control problems by means of neural rough differential equations
(Neural RDEs) introduced in Morrill et al. (2021). Non-Markovianity naturally
arises in control problems due to the time delay effects in the system
coefficients or the driving noises, which leads to optimal control strategies
depending explicitly on the historical trajectories of the system state. By
modelling the control process as the solution of a Neural RDE driven by the
state process, we show that the control-state joint dynamics are governed by an
uncontrolled, augmented Neural RDE, allowing for fast Monte-Carlo estimation of
the value function via trajectories simulation and memory-efficient
backpropagation. We provide theoretical underpinnings for the proposed
algorithmic framework by demonstrating that Neural RDEs serve as universal
approximators for functions of random rough paths. Exhaustive numerical
experiments on non-Markovian stochastic control problems are presented, which
reveal that the proposed framework is time-resolution-invariant and achieves
higher accuracy and better stability in irregular sampling compared to existing
RNN-based approaches.

提出一种基于神经粗糙微分方程的新框架，用于解决非马尔可夫随机控制问题，通过演示控制过程作为神经粗糙微分方程的解的模型来展示控制 - 状态联合动力学如何通过一个未受控的增量神经粗糙微分方程进行管理，同时通过演示神经粗糙微分方程是随机不平滑路径函数的通用近似器来提供理论支撑，实验结果显示，这种方法比现有的基于 RNN 的方法在不规则采样下具有更高的精度和稳定性。

一种用于连续非马尔可夫随机控制问题的神经 RDE 方法

A Neural RDE approach for continuous-time non-Markovian stochastic  control problems

We address the problem of quantifying the non-Markovian character of quantum
time-evolutions of general systems in contact with an environment. We introduce
two different measures of non-Markovianity that exploit the specific traits of
quantum correlations and are suitable for opposite experimental contexts. When
complete tomographic knowledge about the evolution is available, our measure
provides a necessary and sufficient condition to quantify strictly the
non-Markovianity. In the opposite case, when no information whatsoever is
available, we propose a sufficient condition for non-Markovianity. Remarkably,
no optimization procedure underlies our derivation, which greatly enhances the
practical relevance of the proposed criteria.

本文提出了两种针对不同实验环境的量化量子系统与环境交互作用的非马尔科夫性的方法，这些方法可以不需要优化过程而准确地测量马尔科夫性，其中一种方法需要完整的演化信息，而另一种方法则只需要最少的信息。