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

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.

arXiv commentAccepted for publication in IEEE Signal Processing Magazine. Limit of 40 references

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• Internal Model-Based Online Optimization
• Local Strong Convexity of Source Localization and Error Bound for Target Tracking under Time-of-Arrival Measurements
• Extrapolation-based Prediction-Correction Methods for Time-varying Convex Optimization
• Robust Online Learning over Networks
• Bounds for the tracking error of first-order online optimization methods
• Personalized incentives as feedback design in generalized Nash equilibrium problems
• tvopt: A Python Framework for Time-Varying Optimization
• Time-Varying Convex Optimization: A Contraction and Equilibrium Tracking Approach
• A Stochastic Operator Framework for Optimization and Learning with Sub-Weibull Errors
• Online Distributed Learning with Quantized Finite-Time Coordination
• A Control Theoretical Approach to Online Constrained Optimization
• Distributed Prediction-Correction ADMM for Time-Varying Convex Optimization