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：现有大多数基于神经网络的随机最优控制问题求解方法采用逆向动态规划原理，其有效性依赖于对潜在状态变量的模拟能力。然而，当面临部分问题中状态变量无法模拟的困境时，需要将状态变量空间离散化并针对每个数据点单独训练神经网络。该方法在处理大规模状态变量空间时计算效率显著下降。本文针对此类随机最优控制问题，提出了一种基于多任务神经网络的高效解决方案。为训练该多任务神经网络，我们创新性地引入了一种动态平衡各任务学习进度的机制。通过实际衍生品定价问题的数值实验证明，本方法性能优于当前最先进的技术方案。