具有不可分惩罚的凸优化的近似消息传递
Approximate message-passing for convex optimization with non-separable penalties
摘要：
我们引入了一个迭代优化计划的凸目标组成的线性损失和不可分离的罚款，基于期望一致性近似和向量近似消息传递（VAMP）算法。具体地说，我们所处理的惩罚是凸的变量的线性变换被确定，一个值得注意的例子是全变差（TV）。我们描述了消息传递算法-通常用于近似推理-和邻近的优化方法之间的连接，并表明我们的计划，作为VAMP，在性质上类似于Cumberman-Rachford分裂，重要的区别是步长自适应设置。最后，我们基准测试我们的VAMP样迭代的性能在电视处罚是有用的问题，即分类任务功能磁共振成像和重建断层扫描，并显示更快的收敛速度比最先进的方法，如FISTA和ADMM在大多数情况下。
英文摘要：
We introduce an iterative optimization scheme for convex objectives consisting of a linear loss and a non-separable penalty, based on the expectation-consistent approximation and the vector approximate message-passing (VAMP) algorithm. Specifically, the penalties we approach are convex on a linear transformation of the variable to be determined, a notable example being total variation (TV). We describe the connection between message-passing algorithms -- typically used for approximate inference -- and proximal methods for optimization, and show that our scheme is, as VAMP, similar in nature to the Peaceman-Rachford splitting, with the important difference that stepsizes are set adaptively. Finally, we benchmark the performance of our VAMP-like iteration in problems where TV penalties are useful, namely classification in task fMRI and reconstruction in tomography, and show faster convergence than that of state-of-the-art approaches such as FISTA and ADMM in most settings.
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