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That looks interesting, do you know what paper talks about the connection between MDL, regret, and weight decay?

I would start with Shannon's information theory and the Wikipedia page on L2/the MDL as a decent starting point.

For the first, there are a few good papers that simplify the concepts even further.

Sorry, I know what MDL and L2 regularization are, I would like the paper that connects them in the way you mentioned