There exists a function satisfying two-sided PL conditions for which GDA dynamics fail to converge by circling the saddle point.
Hybrid block successive approximation for one-sided non-convex min-max problems: algorithms and applications.IEEE Transactions on Signal Processing, 68:3676–3691, 2020
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PL conditions do not guarantee convergence of gradient descent-ascent dynamics
There exists a function satisfying two-sided PL conditions for which GDA dynamics fail to converge by circling the saddle point.