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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.