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The Douglas Rachford algorithm is an algorithm that converges to a minimizerof a sum of two convex functions. The algorithm consists in fixed pointiterations involving computations of the proximity operators of the twofunctions separately. The paper investigates a stochastic version of thealgorithm where both functions are random and the step size is constant. Weestablish that the iterates of the algorithm stay close to the set of solutionwith high probability when the step size is small enough. Application tostructured regularization is considered.

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