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- W3034307907 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 convex-concave 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/non-concave 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." @default.
- W3034307907 created "2020-06-19" @default.
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- W3034307907 date "2021-07-01" @default.
- W3034307907 modified "2023-10-16" @default.
- W3034307907 title "The limits of min-max optimization algorithms: Convergence to spurious non-critical sets" @default.
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