关键词：统计学习；机器学习；凸优化；自适应；梯度
摘 要：In this thesis, we consider the fundamental questions that arise when trading between multiple such criteria--computation, communication, privacy--while maintaining statistical performance. Can we develop lower bounds that show there must be tradeoffs? Can we develop new procedures that are both theoretically optimal and practically useful? To answer these questions, we explore examples from optimization, confidentiality preserving statistical inference, and distributed estimation under communication constraints. Viewing our examples through a general lens of constrained minimax theory, we prove fundamental lower bounds on the statistical performance of any algorithm subject to the constraints--computational, confidentiality, or communication--specified. These lower bounds allow us to guarantee the optimality of the new algorithms we develop addressing the additional criteria we consider, and additionally, we show some of the practical benefits that a focus on multiple optimality criteria brings.