A Constant Step Stochastic Douglas-Rachford Algorithm with Application to Non Separable Regularizations

Adil Salim 1 Pascal Bianchi 2 Walid Hachem 1
1 COMNUM - Communications Numériques
LTCI - Laboratoire Traitement et Communication de l'Information
2 S2A - Signal, Statistique et Apprentissage
LTCI - Laboratoire Traitement et Communication de l'Information
Abstract : The Douglas Rachford algorithm is an algorithm that converges to a minimizer of a sum of two convex functions. The algorithm consists in fixed point iterations involving computations of the proximity operators of the two functions separately. The paper investigates a stochastic version of the algorithm where both functions are random and the step size is constant. We establish that the iterates of the algorithm stay close to the set of solution with high probability when the step size is small enough. Application to structured regularization is considered.
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Submitted on : Tuesday, November 19, 2019 - 11:22:17 AM
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  • HAL Id : hal-02369904, version 1
  • ARXIV : 1804.00934

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Adil Salim, Pascal Bianchi, Walid Hachem. A Constant Step Stochastic Douglas-Rachford Algorithm with Application to Non Separable Regularizations. 2019. ⟨hal-02369904⟩

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