Convergence of a Piggyback-style method for the differentiation of solutions of standard saddle-point problems

Lea Bogensperger (1) , Antonin Chambolle (2) , Thomas Pock (1)

1 ICG - Institute for Computer Graphics and Vision [Graz]
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We analyse a "piggyback"-style method for computing the derivative of a loss which depends on the solution of a convex-concave saddle point problems, with respect to the bilinear term. We attempt to derive guarantees for the algorithm under minimal regularity assumption 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.

Mots clés: First-order methods; saddle-point problems; differentiation; adjoint methods; piggyback algorithm; learning

Domaines: Analyse numérique [math.NA]; Intelligence artificielle [cs.AI]

Lea Bogensperger, Antonin Chambolle, Thomas Pock. Convergence of a Piggyback-style method for the differentiation of solutions of standard saddle-point problems. SIAM Journal on Mathematics of Data Science, 2022, 4 (3), pp.1003-1030. ⟨10.1137/21M1455887⟩. ⟨hal-03516542v2⟩