Robust learning for optimization: navigating samples and noise

Abstract

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.