In this paper, we focus on the solution of online optimization problems that arise often in signal processing and machine learning, in which we have access to streaming sources of data. We discuss algorithms for online optimization based on the prediction-correction paradigm, both in the primal and dual space. In particular, we leverage the typical regularized least-squares structure appearing in many signal processing problems to propose a novel and tailored prediction strategy, which we call extrapolation-based. By using tools from operator theory, we then analyze the convergence of the proposed methods as applied both to primal and dual problems, deriving an explicit bound for the tracking error, that is, the distance from the time-varying optimal solution. We further discuss the empirical performance of the algorithm when applied to signal processing, machine learning, and robotics problems.

翻译：摘要：本文聚焦于信号处理与机器学习中常见的在线优化问题的求解，此类问题需处理流式数据源。我们基于预测校正范式，在原始空间与对偶空间分别讨论了在线优化算法。特别地，借鉴信号处理问题中常见的正则化最小二乘结构，提出了一种新型定制化预测策略——外推法。通过运用算子理论工具，我们分析了所提方法在原始问题与对偶问题中的收敛性，推导出跟踪误差（即时变最优解的距离）的显式上界。进一步地，我们讨论了该算法在信号处理、机器学习及机器人学问题中的实证表现。