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Conference Papers Year : 2021

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

Abstract

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.
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Dates and versions

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

Identifiers

  • HAL Id : hal-03043862 , version 1

Cite

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⟩
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