Convergence of a Piggyback-Style Method for the Differentiation of Solutions of Standard Saddle-Point Problems

We analyze a “piggyback''-style method for computing the derivative of a loss which depends on the solution of a convex-concave saddle-point problem, with respect to the bilinear term. We attempt to derive guarantees for the algorithm under minimal regularity assumptions on the functions. Our final convergence results include possibly nonsmooth objectives. We illustrate the versatility of the proposed piggyback algorithm by learning optimized shearlet transforms, which are a class of popular sparsifying transforms in the field of imaging