Regularized Nonlinear Acceleration

Damien Scieur (1) , Alexandre d'Aspremont (2) , Francis Bach (1)

1 SIERRA - Statistical Machine Learning and Parsimony
2 LIENS - Laboratoire d'informatique de l'école normale supérieure

We describe a convergence acceleration technique for generic optimization problems. Our scheme computes estimates of the optimum from a nonlinear average of the iterates produced by any optimization method. The weights in this average are computed via a simple linear system, whose solution can be updated online. This acceleration scheme runs in parallel to the base algorithm, providing improved estimates of the solution on the fly, while the original optimization method is running. Numerical experiments are detailed on classical classification problems.

Domaines: Optimisation et contrôle [math.OC]

Damien Scieur, Alexandre d'Aspremont, Francis Bach. Regularized Nonlinear Acceleration. Mathematical Programming, 2018, ⟨10.1007/s10107-018-1319-8⟩. ⟨hal-01384682v2⟩