This dissertation presents novel advancements in the field of continuous nonlinear optimization, focusing on the development of efficient second-order methods for second-order conic programs (SOCPs) and continuous nonlinear two-stage optimization problems. The primary focus is on the theory and computations of Sequential Quadratic Programming (SQP) methods, which are widely used...
Recommender systems (RSs) have become essential tools that provide personalized recommendations to their users. These systems may consider user, item provider, and system requirements simultaneously. With the inclusion of possibly clashing considerations, there is a growing focus on solving multiple-objective recommender system (MORS) problems as efficiently as possible. The constrained...
In reinforcement learning (RL), an agent aims to learn the optimal policy by interacting with the environment and collecting the reward for each action taken. With the aid of strong function approximators such as the neural networks, RL achieves tremendous empirical successes in various scenarios, including game playing \citep{silver2016mastering, silver2017mastering},...
While deep reinforcement learning achieves tremendous successes in practice, its efficiencies are rarely understood in theory. The dissertation contains three parts, with each part corresponding to the study of an independent theoretical reinforcement learning problem. The three parts in all discuss the mechanism of how (deep) reinforcement learning efficiently solves...
This thesis develops novel methods for generating space-filling designs inside a designspace and subsampling from a data set. It incorporates materials from two papers by the
author: Shang and Apley 2021; Shang, Apley, and Mehrotra 2022a. Chapter 1 discusses space-filling designs of computer experiments, which is publishedas Shang and Apley...
In this dissertation, we aim to develop algorithms that achieve optimality with provable complexity guarantees under various settings in reinforcement learning (RL). Specifically, in Markov decision processes (MDPs), we study single-agent and multi-agent online RL, respectively, and offline RL under the presence of unobserved confounders. Single-agent online RL. We design...
In this dissertation, we aim to develop efficient algorithms with theoretical guarantees for several data-driven decision making problems. Specifically, we study the data-driven deci- sion making from three different perspectives: statistical learning, nonconvex optimization, and control of stochastic system. This dissertation contains three parts. In the first part, we study...
In this thesis, we aim to develop efficient algorithms with theoretical guarantees for noisy nonlinear optimization problems, with and without constraints, under various different assumptions. Apart from Chapter 1 which provides relevant backgrounds, the remaining of thesis is divided into four chapters. In Chapter 2, we establish the theoretical convergence...
Massive amounts of data with a large number of predictors routinely arrive in data systems as a result of recent developments in data collection technology. In this data-intensive world, predictive models are more important than ever to extract information and make decisions, and are widely applied in many different fields....
Multistage optimization is a prominent modeling tool to solve a broad range of dynamic decision-making problems in the presence of uncertainty. However, computing optimal policies is intractable, since they are obtained by considering all possible realizations of uncertainties and subsequent future decisions over time. To overcome these challenges, we present...