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Given that policies are probability distributions, in principle, you can use any metric or measure of distance that can be used to compare two probability distributions. (Note that notions of distance are not necessarily metrics in a mathematical sense). A common measure is the Kullback–Leibler divergence (which is not a metric, in a mathematical sense, ...

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I don't have a definite answer, but only a suspicion/idea: Looking at Figure 1 from the WGAN paper, we clear see that the JS divergence on the right is not continuous at $0$, hence not differentiable at $0$. However, the EM plot on the left is continuous also at $0$. You could now argue that we have a kink there, so it should not be differentiable there ...

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This question is very general in the sense that the reason may differ depending on the area of ML you are considering. Below are two different areas of ML where the KL-divergence is a natural consequence: Classification: maximizing the log-likelihood (or minimizing the negative log-likelihood) is equivalent to minimizing KL divergence as typical used in DL-...

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In ML we always deal with unknown probability distributions from which the data comes. The most common way to calculate the distance between real and model distribution is $KL$ divergence. Why Kullback–Leibler divergence? Although there are other loss functions (e.g. MSE, MAE), $KL$ divergence is natural when we are dealing with probability distributions. It ...

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