Most existing neural network-based approaches for solving stochastic optimal control problems using the associated backward dynamic programming principle rely on the ability to simulate the underlying state variables. However, in some problems, this simulation is infeasible, leading to the discretization of state variable space and the need to train one neural network for each data point. This approach becomes computationally inefficient when dealing with large state variable spaces. In this paper, we consider a class of this type of stochastic optimal control problems and introduce an effective solution employing multitask neural networks. To train our multitask neural network, we introduce a novel scheme that dynamically balances the learning across tasks. Through numerical experiments on real-world derivatives pricing problems, we prove that our method outperforms state-of-the-art approaches.

翻译：现有基于神经网络的求解随机最优控制问题的方法大多依赖于后向动态规划原理，并需要能够模拟底层状态变量。然而，在某些问题中，这种模拟不可行，导致需要将状态变量空间离散化，并对每个数据点训练一个神经网络。当处理大规模状态变量空间时，此类方法在计算上效率低下。本文针对该类随机最优控制问题中的一类问题，提出了一种采用多任务神经网络的有效解决方案。为了训练多任务神经网络，我们引入了一种新颖的机制，能够动态平衡各任务间的学习过程。通过对真实衍生产品定价问题的数值实验，我们证明了该方法优于现有最先进技术。