2023 Theses Doctoral

Topics in Deep Learning and Data-driven Optimization

Bahamou, Achraf

Data-driven optimization has become an increasingly popular approach for solving complex problems in various domains, such as finance, online retail, and engineering. However, in many real-world applications, the amount of available data can vary significantly, ranging from limited to large data sets. Both of these regimes present unique modeling and optimization challenges.

In this thesis, we explore two distinct problems in two different data availability and model complexity regimes. In the first part (Chapters 2 and 3), we focus on the development of novel optimization algorithms for training deep neural network (DNN) models on large data sets, in particular, we develop practical optimization methods that incorporate curvature information in an economical way to accelerate the optimization process. The performance of the proposed methods is compared to that of several state-of-the-art methods used to train DNNs, to validate their effectiveness both in terms of time efficiency and generalization power.

In the second part of the dissertation (Chapters 4), we focus on data-driven pricing in the limited data regime. More specifically, we study the fundamental problem of a seller pricing a product based on historical information consisting of the observed demand at a single historical price point. We develop a novel framework that allows characterizing optimal performance for deterministic or more general randomized mechanisms and leads to fundamental novel insights on the value of limited demand data for pricing.