There exists a function satisfying two-sided PL conditions for which GDA dynamics fail to converge by circling the saddle point.
Provably convergent quasistatic dynamics for mean-field two-player zero-sum games
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math.OC 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
For certain double-well payoff functions with strong coupling and small noise, the mean-field Langevin descent-ascent flow stays near a limit cycle and fails to converge.
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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.
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Oscillating solutions to the mean-field Langevin descent-ascent flow
For certain double-well payoff functions with strong coupling and small noise, the mean-field Langevin descent-ascent flow stays near a limit cycle and fails to converge.