Approximate message-passing for convex optimization with non-separable penalties

Abstract : 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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https://hal-cea.archives-ouvertes.fr/cea-01932983
Contributor : Emmanuelle de Laborderie <>
Submitted on : Friday, November 23, 2018 - 2:35:06 PM
Last modification on : Wednesday, May 15, 2019 - 3:39:37 AM

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  • HAL Id : cea-01932983, version 1
  • ARXIV : 1809.06304

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Andre Manoel, Florent Krzakala, Bertrand Thirion, Gaël Varoquaux, Lenka Zdeborová. Approximate message-passing for convex optimization with non-separable penalties. 2018. ⟨cea-01932983⟩

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