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About this paper
Chi Jin, Rong Ge, Praneeth Netrapalli, Sham M. Kakade, Michael I. Jordan
PGD adds occasional random perturbations to gradient descent to help escape saddle points. When the gradient becomes small, it nudges the current point, then resumes ordinary updates. Under smoothness assumptions, they prove it reaches approximate second-order stationarity in nearly the first-order iteration count, up to logarithmic factors. This is an iteration bound, not a runtime result or guarantee of a local minimum.
Summary by alphaXiv.
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