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I'm using an AdamOptimizer, and I compute the gradients, but before applying the descent step, I scale (i.e.: multiply) gradients with constants, to mimic having a different learning rate per parameter instead. Is this equivalent to having a learning rate per parameter?

Staring at the formulas of Adam, I believe they might be the same, although it have the impression my results are not the same, when using multiple optimizers, each with their own learning-rate parameter.

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