Perhaps a log-log plot would be better. Q2: Please summarize your review in 1-2 sentences This is a well-written and clear paper, but I think the proposed method is well understood by the graphical models community and is not that original. I also feel that the experiments section was not objective enough - both the strengths and the weakness of a method need to be discussed by the authors.

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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper proposes an algorithm for online combinatorial optimization. In this online learning problem, the action space is combinatorially large and can be represented in a d-dimensional Euclidean space such that the loss in each time step is a linear function of the action. It would greatly improve the paper if there was a thorough comparison between the new algorithm and Online Stochastic Mirror Descent (OSMD by Audibert et al., [3] in the current paper) both in terms of how the algorithms work and in terms of regret bounds. In the current form of the paper, I am not sure if the new algorithm is significantly different from OSMD or if it improves its bounds.

Regularization is typically understood as improving generalization by altering the landscape of local extrema to which the model eventually converges.

The coding rate can be accurately computed from finite samples of degenerate subspace-like distributions and can learn intrinsic representations in supervised, self-supervised, and unsupervised settings in a unified manner.

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