A probabilistic incremental proximal gradient method

Ömer Deniz Akyildiz (1) , Emilie Chouzenoux (2, 3) , Víctor Elvira (4, 5) , Joaquín Míguez (1)

1 UC3M - Universidad Carlos III de Madrid [Madrid]
2 GALEN-POST - Organ Modeling through Extraction, Representation and Understanding of Medical Image Content
3 OPIS - OPtimisation Imagerie et Santé
4 Institut TELECOM/TELECOM Lille1
5 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189

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.

Keywords: Stochastic gradient; Extended Kalman filtering; Probabilistic optimization; Proximal algorithms

Domains: Signal and Image processing

Ömer Deniz Akyildiz, Emilie Chouzenoux, Víctor Elvira, Joaquín Míguez. A probabilistic incremental proximal gradient method. IEEE Signal Processing Letters, 2019, 26 (8), pp.1257-1261. ⟨10.1109/LSP.2019.2926926⟩. ⟨hal-01946642⟩