The paper introduces (L,\bar L)-anisotropic smoothness and proves O(1/K) convergence rates for nonlinearly preconditioned gradient methods, unifying gradient clipping, Adam, and Adagrad under one theory.
Therefore, through (Bauschke et al., 2017b, Proposition 11.7) we get thath ∗ is increasing onR +
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Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness
The paper introduces (L,\bar L)-anisotropic smoothness and proves O(1/K) convergence rates for nonlinearly preconditioned gradient methods, unifying gradient clipping, Adam, and Adagrad under one theory.