Optimization and Learning with Information Streams: Time-varying Algorithms and Applications

TL;DR

This paper reviews and analyzes time-varying optimization algorithms designed for streaming data, emphasizing their application in machine learning, signal processing, and control, highlighting their robustness, convergence, and distributed computation aspects.

Contribution

It introduces and discusses design principles for online first-order optimization methods that handle gradient errors and compares their performance to batch algorithms in streaming contexts.

Findings

Algorithms can perform poorly online despite batch convergence guarantees.

Distributed computation enhances scalability and robustness.

Numerical examples demonstrate practical effectiveness.

Abstract

There is a growing cross-disciplinary effort in the broad domain of optimization and learning with streams of data, applied to settings where traditional batch optimization techniques cannot produce solutions at time scales that match the inter-arrival times of the data points due to computational and/or communication bottlenecks. Special types of online algorithms can handle this situation, and this article focuses on such time-varying optimization algorithms, with emphasis on Machine Leaning and Signal Processing, as well as data-driven Control. Approaches for the design of time-varying or online first-order optimization methods are discussed, with emphasis on algorithms that can handle errors in the gradient, as may arise when the gradient is estimated. Insights on performance metrics and accompanying claims are provided, along with evidence of cases where algorithms that are provably convergent in batch optimization may perform poorly in an online regime. The role of distributed computation is discussed. Illustrative numerical examples for a number of applications of broad interest are provided to convey key ideas.