Structure-Driven Algorithm Design in Optimization and Machine Learning

A textbook property of optimization algorithms is their ability to optimize problems under generic regularity conditions. However, the performance of these fundamental and general-purpose optimization algorithms is often unsatisfactory; indeed, for many real problems, the gains from leveraging special structures can be huge.

A basic question then arises: how can we harness problem-specific structure within our algorithms to obtain fast, practical algorithms with strong performance guarantees? Although this line of research – which has been studied extensively for over 70 years – has enjoyed widespread success, the recent reliable and/or multi-agent machine-learning success stories have introduced new formulations ripe for deep theoretical analysis and remarkable practical impact.