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arXiv · 1812.01655

A probabilistic incremental proximal gradient method

Ömer Deniz Akyildiz·Émilie Chouzenoux·Víctor Elvira·Joaquín Míguez
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Abstract

In this paper, we propose a probabilistic optimization method, named probabilistic incremental proximal gradient (PIPG) method, by developing a probabilistic interpretation of the incremental proximal gradient algorithm. We explicitly model the update rules of the incremental proximal gradient method and develop a systematic approach to propagate the uncertainty of the solution estimate over iterations. The PIPG algorithm takes the form of Bayesian filtering updates for a state-space model constructed by using the cost function. Our framework makes it possible to utilize well-known exact or approximate Bayesian filters, such as Kalman or extended Kalman filters, to solve large-scale regularized optimization problems.

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BibTeXRIS

Ömer Deniz Akyildiz, Émilie Chouzenoux, Víctor Elvira, Joaquín Míguez. 2018-12-04. A probabilistic incremental proximal gradient method. https://arxiv.org/abs/1812.01655

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