增量近端法：概率论视角
The Incremental Proximal Method: A Probabilistic Perspective
摘要：
在这项工作中，我们强调的增量邻近方法和随机滤波器之间的连接。我们首先表明，最近的运营商一致，因此可以实现，贝叶斯更新。我们给出了线性回归问题的更新的显式形式，并证明了当先验和似然是高斯时，最小二乘回归的邻近算子和贝叶斯更新之间存在一一对应关系。然后，我们进行观察，一般顺序设置：我们考虑的增量邻近的方法，这是一个大规模的优化算法，并表明，对于一个线性二次成本函数，它可以自然地实现卡尔曼滤波器。然后，我们讨论了这一想法的影响，非线性优化问题的邻近运营商一般是不可实现的。在这样的设置中，我们认为，扩展卡尔曼滤波器可以提供一个系统的方法来推导的实际程序。
英文摘要：
In this work, we highlight a connection between the incremental proximal method and stochastic filters. We begin by showing that the proximal operators coincide, and hence can be realized with, Bayes updates. We give the explicit form of the updates for the linear regression problem and show that there is a one-to-one correspondence between the proximal operator of the least-squares regression and the Bayes update when the prior and the likelihood are Gaussian. We then carry out this observation to a general sequential setting: We consider the incremental proximal method, which is an algorithm for large-scale optimization, and show that, for a linear-quadratic cost function, it can naturally be realized by the Kalman filter. We then discuss the implications of this idea for nonlinear optimization problems where proximal operators are in general not realizable. In such settings, we argue that the extended Kalman filter can provide a systematic way for the derivation of practical procedures.
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