Noisy Optimization and Online Prediction

: Approaches of Gradient Descent and State-space Models

Abstract

This thesis focuses on noisy optimization problems and online prediction in nonstationary environment using Gaussian time-varying linear models. For noisy optimization problems, we propose an algorithm based on gradient descent and its extension to Nesterov's gradient descent. We also study the convergence properties of stochastic gradient descent with step-sizes determined by backtracking line search. For the online prediction problem, we propose an approach by converting a Bayesian model to a state-space model and using Kalman filter to make predictions recursively.

Date of Award	10 Dec 2024
Original language	English
Awarding Institution	University of Bristol
Supervisor	Mathieu Gerber (Supervisor) & Nina C Snaith (Supervisor)