Optimization and Learning with Information Streams: Time-varying Algorithms and Applications
This work tackles the problem of real-time data processing for researchers and practitioners in machine learning, signal processing, and control, but it is incremental as it reviews and discusses existing time-varying optimization approaches.
The paper addresses the challenge of applying optimization and learning algorithms to streaming data where traditional batch methods are too slow, focusing on time-varying first-order methods that can handle gradient errors. It provides insights on performance metrics and illustrates cases where batch-convergent algorithms fail in online settings, supported by numerical examples.
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.