I am looking at the following paper to implement dual decomposition for my algorithm: http://www.csd.uoc.gr/~komod/publications/docs/DualDecomposition_PAMI.pdf
On Pg.29 they suggest setting the step size for the sub-gradient method by taking the difference of the best primal solution and current dual solution and dividing by the L2-norm of the sub-gradient at current iteration.
My doubt is the following: Do I use sub-gradients for each slave problem and compute a different step-size for each slave problem? Or is there some way I can compute the sub-gradient for the combined dual problem?