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arXiv · 1804.04529

Online convex optimization and no-regret learning: Algorithms, guarantees and applications

E. Veronica Belmega·Panayotis Mertikopoulos·Romain Negrel·Luca Sanguinetti
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Abstract

Spurred by the enthusiasm surrounding the "Big Data" paradigm, the mathematical and algorithmic tools of online optimization have found widespread use in problems where the trade-off between data exploration and exploitation plays a predominant role. This trade-off is of particular importance to several branches and applications of signal processing, such as data mining, statistical inference, multimedia indexing and wireless communications (to name but a few). With this in mind, the aim of this tutorial paper is to provide a gentle introduction to online optimization and learning algorithms that are asymptotically optimal in hindsight - i.e., they approach the performance of a virtual algorithm with unlimited computational power and full knowledge of the future, a property known as no-regret. Particular attention is devoted to identifying the algorithms' theoretical performance guarantees and to establish links with classic optimization paradigms (both static and stochastic). To allow a better understanding of this toolbox, we provide several examples throughout the tutorial ranging from metric learning to wireless resource allocation problems.

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E. Veronica Belmega, Panayotis Mertikopoulos, Romain Negrel, Luca Sanguinetti. 2018-04-12. Online convex optimization and no-regret learning: Algorithms, guarantees and applications. https://arxiv.org/abs/1804.04529

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