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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The authors present a framework for online optimization of non-decomposable loss functions (those that do not decompose as a sum over data points). Their idea is to write L_t(w) = l(w, x_{1:t}) - l(w, x_{1:t-1}). While L_t(w) in general will not be convex, its cumulative sum will be, which turns out to be enough for the FTRL analysis to hold. However, we still need to establish stability properties for L_t(w), which is harder than for decomposable loss functions.