There exists a function satisfying two-sided PL conditions for which GDA dynamics fail to converge by circling the saddle point.
Linear convergence of gradient and proximal-gradient methods under the Polyak-Łojasiewicz condition
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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.