The limits of min-max optimization algorithms: Convergence to spurious non-critical sets - Archive ouverte HAL
Communication Dans Un Congrès Année : 2021

The limits of min-max optimization algorithms: Convergence to spurious non-critical sets

Résumé

Compared to minimization problems, the min-max landscape in machine learning applications is considerably more convoluted because of the existence of cycles and similar phenomena. Such oscillatory behaviors are well-understood in the convexconcave regime, and many algorithms are known to overcome them. In this paper, we go beyond the convex-concave setting and we characterize the convergence properties of a wide class of zeroth-, first-, and (scalable) second-order methods in non-convex/nonconcave problems. In particular, we show that these state-of-the-art min-max optimization algorithms may converge with arbitrarily high probability to attractors that are in no way min-max optimal or even stationary. Spurious convergence phenomena of this type can arise even in two-dimensional problems, a fact which corroborates the empirical evidence surrounding the formidable difficulty of training GANs.
Fichier principal
Vignette du fichier
SpuriousMinMax.pdf (3.48 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03043862 , version 1 (07-12-2020)

Identifiants

  • HAL Id : hal-03043862 , version 1

Citer

Ya-Ping Hsieh, Panayotis Mertikopoulos, Volkan Cevher. The limits of min-max optimization algorithms: Convergence to spurious non-critical sets. ICML 2021 - 38th International Conference on Machine Learning, Jul 2021, Vienna, Austria. ⟨hal-03043862⟩
99 Consultations
300 Téléchargements

Partager

More