We propose an implementable, feedforward neural network-based structure preserving probabilistic numerical approximation for a generalized obstacle problem describing the value of a zero-sum differential game of optimal stopping with asymmetric information. The target solution depends on three variables: the time, the spatial (or state) variable, and a variable from a standard $(I-1)$-simplex which represents the probabilities with which the $I$ possible configurations of the game are played. The proposed numerical approximation preserves the convexity of the continuous solution as well as the lower and upper obstacle bounds. We show convergence of the fully-discrete scheme to the unique viscosity solution of the continuous problem and present a range of numerical studies to demonstrate its applicability.

翻译：我们提出一种基于前馈神经网络、可实现的保结构概率数值逼近方法，用于求解描述具有非对称信息的最优停时零和微分博弈值的一类广义障碍问题。目标解依赖于三个变量：时间变量、空间（或状态）变量，以及标准$(I-1)$-单纯形中的变量，该变量表示博弈的$I$种可能构型被选择的概率。所提出的数值逼近方法保留了连续解的凸性以及上下障碍界。我们证明了全离散格式收敛于连续问题的唯一黏性解，并通过一系列数值实验验证了该方法的适用性。