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

TL;DR

This paper introduces online convex optimization and no-regret learning algorithms, emphasizing their theoretical guarantees and practical applications in data-driven fields like signal processing and wireless communications.

Contribution

It provides a comprehensive tutorial on online optimization algorithms, highlighting their asymptotic optimality, theoretical guarantees, and connections to classic optimization methods.

Findings

Algorithms approach the performance of an all-knowing virtual algorithm

Theoretical guarantees are established for various algorithms

Applications include metric learning and wireless resource management

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.