An adaptive SAM variant using AdaGrad and Adam steps for both perturbation and update is claimed to converge at O(ln T / T^{1/4}) without tuning, but the Adam version still needs decaying hyperparameters and the proof contains an incorrect inequality.
Convergence of adagrad for non-convex objectives: Simple proofs and relaxed assumptions,
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LightSAM: Parameter-Agnostic Sharpness-Aware Minimization
An adaptive SAM variant using AdaGrad and Adam steps for both perturbation and update is claimed to converge at O(ln T / T^{1/4}) without tuning, but the Adam version still needs decaying hyperparameters and the proof contains an incorrect inequality.