Model with multi variable target

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Hi all. I need to train a model in which the target is a probability vector, i,e [0.2, 0.4. 0.1, 0.3] such that the sum of its components is 1. I am thinking of using classifier with cross entropy loss, but i am not sure that this is the right solution because such classifiers are usually fitted against a target with [0,0,1,0...] i.e - only one component equals to 1 and then it can be shown that the classifier in fact learn to generate a distribution with highest values on the classifier best candidate. I need something similar but not the same, i.e a model with a loss function of kl-divergence or something like "distance" between probability vectors, any ideas or references?

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