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.

本研究论文采用多任务神经网络的有效解法，通过数值实验，证明其在处理实际金融衍生品定价问题上优于现有方法。

深度多任务神经网络解决一些随机最优控制问题

Deep multitask neural networks for solving some stochastic optimal  control problems

We present a novel $Q$-learning algorithm to solve distributionally robust
Markov decision problems, where the corresponding ambiguity set of transition
probabilities for the underlying Markov decision process is a Wasserstein ball
around a (possibly estimated) reference measure. We prove convergence of the
presented algorithm and provide several examples also using real data to
illustrate both the tractability of our algorithm as well as the benefits of
considering distributional robustness when solving stochastic optimal control
problems, in particular when the estimated distributions turn out to be
misspecified in practice.

我们提出了一种新的 $Q$-learning 算法，用于解决分配鲁棒的马尔可夫决策问题。我们证明了算法的收敛性，并提供了几个示例来说明我们算法的可处理性以及考虑分布稳健性在解决随机最优控制问题时的好处，尤其是在实践中估计的分布出现错误时。