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.

The use of Machine Learning (ML) has become increasingly central to the acquisition and interpretation of data. As improved methodologies for training ML models are created, the performance of models trained with these methodologies are inevitably compared to the field's moonshot: Artificial General Intelligence. However, today's models fall far short of the ability to generalize robustly on multiple tasks, let alone be fully generalizable. To address the shortcomings of modern ML architectures, we've turned for inspiration to the human brain. Specifically, we sought to emulate the sparse, hierarchical structure of the human cortex, which enables the flexible learning and multitask performance that we humans are lucky enough to possess.

Multitask learning (MTL) is a learning paradigm in which multiple tasks are learned jointly, aiming to improve the performance of individual tasks by sharing information across tasks [4, 26], using various information sharing mechanisms. For example, MTL models based on deep neural networks commonly use shared hidden layers for all the tasks; probabilistic MTL models are usually based on shared priors over the parameters of the multiple tasks [16, 5]; Gaussian Process based models, e.g., multitask Gaussian Processes (GP) and extensions [2, 23], commonly employ covariance functions that models both inputs and task similarity. Multi-label, multi-class, multi-output learning can be seen as special cases of multitask learning where each task has the same set of inputs. Transfer learning is also similar to MTL, except that the objective of MTL is to improve the performance over all the tasks whereas the objective of transfer learning is to usually improve the performance of a target task by leveraging information from source tasks [26]. Zero-shot learning and few-shot learning are also closely related to MTL. Prior works [14, 24] have shown that a fully connected Bayesian neural network (NN) [13, 15] with a single, infinitely-wide hidden layer, with independent and identically distributed (i.i.d) priors on weights, is equivalent to a Gaussian Process. The result has recently been also generalized to deep Bayesian neural networks [9] with any number of hidden layers. These connections between Bayesian neural networks and GP offer many benefits, such as theoretical understanding of neural networks, efficient Bayesian inference for deep NN by learning the equivalent GP, etc. Motivated by the equivalence of deep Bayesian neural networks and GP, in this work, we investigate whether a similar connection exists between deep multitask Bayesian neural networks [18] and multitask Gaussian Processes