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The boundary control problem is a non-convex optimization and control problem in many scientific domains, including fluid mechanics, structural engineering, and heat transfer optimization. The aim is to find the optimal values for the…
Tensor networks (TN) have found a wide use in machine learning, and in particular, TN and deep learning bear striking similarities. In this work, we propose the quantum-classical hybrid tensor networks (HTN) which combine tensor networks…
This paper presents preliminary work on using deep neural networks to guide general-purpose heuristic algorithms for performing utilitarian combinatorial assignment. In more detail, we use deep learning in an attempt to produce heuristics…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
Solving nonlinear optimal control problems is a challenging task, particularly for high-dimensional problems. We propose algorithms for model-based policy iterations to solve nonlinear optimal control problems with convergence guarantees.…
The application of machine learning techniques to solve problems in quantum control together with established geometric methods for solving optimisation problems leads naturally to an exploration of how machine learning approaches can be…
The performance of deep neural networks (DNN) is very sensitive to the particular choice of hyper-parameters. To make it worse, the shape of the learning curve can be significantly affected when a technique like batchnorm is used. As a…
This work studies the deep learning-based numerical algorithms for optimal hedging problems in markets with general convex transaction costs on the trading rates, focusing on their scalability of trading time horizon. Based on the…
The recent surge in Deep Learning (DL) research of the past decade has successfully provided solutions to many difficult problems. The field of quantitative analysis has been slowly adapting the new methods to its problems, but due to…
Deep learning is mainly based on utilizing gradient-based optimization for training Deep Neural Network (DNN) models. Although robust and widely used, gradient-based optimization algorithms are prone to getting stuck in local minima. In…
We develop a deep learning algorithm for constructing globally accurate approximations to functional rational expectations equilibria of dynamic stochastic economies in the sequence space. We use deep neural networks to parameterize key…
This paper highlights new opportunities for designing large-scale machine learning systems as a consequence of blurring traditional boundaries that have allowed algorithm designers and application-level practitioners to stay -- for the most…
Deep neural networks (NNs) encounter scalability limitations when confronted with a vast array of neurons, thereby constraining their achievable network depth. To address this challenge, we propose an integration of tensor networks (TN)…
Optimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton-Jacobi-Bellman equations. Building on recent machine learning inspired approaches towards high-dimensional PDEs, we investigate the…
In this paper, we first conduct a study of the portfolio selection problem, incorporating both exogenous (proportional) and endogenous (resulting from liquidity risk, characterized by a stochastic process) transaction costs through the…
Q-learning is a popular reinforcement learning algorithm. This algorithm has however been studied and analysed mainly in the infinite horizon setting. There are several important applications which can be modeled in the framework of finite…
The numerical solution of high dimensional partial differential equations (PDEs) is severely constrained by the curse of dimensionality (CoD), rendering classical grid--based methods impractical beyond a few dimensions. In recent years,…
The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…
This paper explores some variations of a hierarchical control framework that has been recently proposed. The framework is dedicated to control a network of interconnected subsystems such as the ones describing cryogenic processes or power…
In insurance mathematics optimal control problems over an infinite time horizon arise when computing risk measures. Their solutions correspond to solutions of deterministic semilinear (degenerate) elliptic partial differential equations. In…