Public defence in Signal Processing and Data Analytics, M.Sc. Endrit Dosti

The title of the thesis: Generalized Accelerated Optimization Framework for Big Data Processing

Thesis defender: Endrit Dosti
Opponent: Prof. Jean-Christophe Pesquet, CentraleSupélec, Université Paris-Saclay, France
Custos: Prof. Sergiy Vorobyov, Aalto University School of Electrical Engineering, Department of Information and Communications Engineering 

The research on development of optimal gradient-based methods dates back to the 1980s, when the Fast Gradient Method (FGM) was first introduced. The method is efficient in achieving a fast convergence rate, while still maintaining a low per-iteration complexity. FGM has gathered significant attention in the recent years due to the need to enable the recent advancements in artificial intelligence and to efficiently process large-scale data. 

FGM's remarkable properties continue to be a subject of intensive study in the optimization community, yet its fundamental rationale remains unknown. Obtaining a better understanding of the framework used for devising FGM can provide insight into building more advanced algorithms that can be used to efficiently solve large-scale optimization problems. 

This study introduces the generalized estimating sequences framework, which represents a mathematical tool that can be applied to construct more efficient gradient-based methods. These methods can be utilized for solving large-scale optimization problems in signal processing, machine learning, and statistics. In this thesis, a new perspective on accelerated first-order methods is given, while more intuition behind their design is provided. Moreover, the usage of the framework allows to present new algorithms for different problem classes, which offer greater efficiency than existing state-of-the-art methods.

Keywords: Large-scale optimization; Estimating sequences; Fast gradient methods; Smooth and convex functions; Composite objectives

Thesis available for public display 10 days prior to the defence at: https://aaltodoc.aalto.fi/doc_public/eonly/riiputus/

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Doctoral theses in the School of Electrical Engineering: https://aaltodoc.aalto.fi/handle/123456789/53