Deep Learning and Optimal Stochastic Control with Applications
Time: Fri 2026-02-06 10.00
Location: Q2, Malvinas väg 10, Stockholm
Subject area: Applied and Computational Mathematics, Mathematical Statistics
Doctoral student: Giulia Pucci , Sannolikhetsteori, matematisk fysik och statistik
Opponent: Professor Huyen Pham,
Supervisor: Associate professor Nacira Agram, Matematik (Avd.), Sannolikhetsteori, matematisk fysik och statistik
QC 2026-01-13
Abstract
This thesis brings together theoretical advances in stochastic optimal control and modern deep learning techniques, with particular emphasis on applications in environmental and energy systems. The first group of contributions investigates optimal control from a theoretical perspective, developing new results and illustrating their relevance through real world applications. The second part explores deep learning methods for solving stochastic differential equations and control problems that are analytically intractable.
We begin by studying impulse control problems for conditional McKean--Vlasov jump diffusions, extending the classical verification theorem to the setting in which the state dynamics depend on their conditional distribution. We then examine an optimal control problem for pollution growth on a spatial network, formulated in a deterministic framework but capturing how environmental policies propagate across interconnected geographical regions. Finally, we develop a model for investment in renewable energy capacity under uncertainty, characterising how optimal installation strategies change in response to fluctuations in energy demand and production. These contributions show how stochastic control can be used to address pressing challenges in environmental regulation and energy planning.
The second line of research focuses on deep learning methods for backward stochastic differential equations (BSDEs) and related formulations, together with direct machine learning approaches for high-dimensional stochastic control. Specifically, we solve Dynkin games by reformulating them as doubly reflected BSDEs, enabling the computation of optimal stopping strategies in energy market contracts. We further develop a deep learning solver for backward stochastic Volterra integral equations (BSVIEs), extending neural BSDE methods to systems with memory. In addition, we propose a machine learning framework for renewable capacity investment under jump uncertainty, treating the problem both through a direct control learning strategy and through a newly developed solver for pure jump BSDEs.
Overall, this thesis lies at the intersection of rigorous mathematical analysis and machine learning-based approaches to stochastic optimal control. On the one hand, we show how careful modeling and theoretical results enable the formulation and study of complex, realistic control problems; on the other hand, we demonstrate how modern machine learning techniques provide powerful tools for solving these problems efficiently. The applications are motivated by urgent questions in environmental and energy sustainability.