Robust learning for optimization: navigating samples and noise

• Main Author: Yang, Chunxue
• Other Authors: Bei Xiaohui
• Format: Thesis-Doctor of Philosophy
• Language: English
• Published: Nanyang Technological University 2023
• Subjects: Science::Mathematics::Applied mathematics::Optimization; Science::Mathematics::Applied mathematics::Game theory; Science::Mathematics::Discrete mathematics::Combinatorics
• Online Access: https://hdl.handle.net/10356/170243
• Institution: Nanyang Technological University

Optimization is the process of identifying the optimal solution among a multitude of options, which lies at the heart of many computational problems in operations research, computer science, and engineering. Traditional optimization methods rely on formulating a model and designing algorithms based on input parameters. However, in practice, acquiring accurate inputs may be impeded by a lack of information, uncertainties in the objective function, or errors in parameter evaluation. This makes designing robust optimization algorithms based on learned instances containing randomness or an oracle in a noisy form an intriguing research direction, which is known as robust learning for optimization. This thesis applies robust learning for optimization to two theoretical computer science domains: auction design and combinatorial optimization, with the goal of developing robust algorithms that can efficiently output near-optimal solutions despite the presence of randomness or noise.