论文标题
基于推断的预测校正方法，用于时变凸优化
Extrapolation-based Prediction-Correction Methods for Time-varying Convex Optimization
论文作者
论文摘要
在本文中，我们专注于在信号处理和机器学习中经常出现的在线优化问题的解决方案，在这些问题中，我们可以访问数据流源。我们根据原始空间和双重空间中的预测校正范式讨论了在线优化的算法。特别是，我们利用许多信号处理问题中出现的典型正规化最小二乘结构来提出一种新颖和量身定制的预测策略，我们称之为基于外推。然后，我们使用操作者理论的工具，然后分析针对原始问题和双重问题所提出的方法的收敛性，从而推导了针对跟踪误差的明确绑定，即与时间变化的最佳解决方案的距离。当应用于信号处理，机器学习和机器人问题问题时，我们进一步讨论了该算法的经验性能。
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.
