Divergence of the ADAM algorithm with fixed-stepsize: a (very) simple example

Ph. L. Toint

Divergence of the ADAM algorithm with fixed-stepsize: a (very) simple example

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arxiv 2308.00720 v1 pith:JPE624IS submitted 2023-08-01 cs.LG

Ph. L. Toint This is my paper · ORCID

classification cs.LG

keywords adamalgorithmdivergencefunctiongradientsimpleveryabsence

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A very simple unidimensional function with Lipschitz continuous gradient is constructed such that the ADAM algorithm with constant stepsize, started from the origin, diverges when applied to minimize this function in the absence of noise on the gradient. Divergence occurs irrespective of the choice of the method parameters.

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On the Convergence of Adam, Revisited
cs.LG 2026-07 accept novelty 7.0 of 10

Projected Adam and listed variants have lim RT/T > 0 for all β1, β2 ∈ [0,1) on a 3-periodic linear online problem with slopes near 2, −1, −1.

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