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Abstract

Classical optimization techniques have found widespread use in machine learning. Convex optimization has
occupied the center-stage and significant effort continues to be still devoted to it. New problems constantly
emerge in machine learning, e.g., structured learning and semi-supervised learning, while at the same time
fundamental problems such as clustering and classification continue to be better understood. Moreover,
machine learning is now very important for real-world problems with massive datasets, streaming inputs,
the need for distributed computation, and complex models. These challenging characteristics of modern
problems and datasets indicate that we must go beyond the traditional optimization approaches common
in machine learning. What is needed is optimization tuned for machine learning tasks. For example, tech-
niques such as non-convex optimization (for semi-supervised learning, sparsity constraints), combinatorial
optimization and relaxations (structured learning), stochastic optimization (massive datasets), decomposi-
tion techniques (parallel and distributed computation), and online learning (streaming inputs) are relevant
in this setting. These techniques naturally draw inspiration from other fields, such as operations research,
polyhedral combinatorics, theoretical computer science, and the optimization community.