50a074e6a8da4662ae0a29edde722179-AuthorFeedback.pdf

In order to help clarify our contributions and or-2 ganize them for readers, we provide the following table to summarize the differences between regrets.3 REVIEWER 4 Thank you for your comments. Concept drift occurs when the optimal model attimetmay no longer bethe optimal model10 at timet+1. Consider an online learning problem with concept drift withT = 3 time periods and loss functions:11 f1(x) = (x 1)2,f2(x) = (x 2)2,f3(x) = (x 3)2. Figure 1: SGD online with momentum Theoretical motivation via Calibration: A more formal motivation of our regret23 can be related to the concept of calibration [1]. The comment on line 110 can be24 rewritten as: If the updates{x1,,xT} are well-calibrated, then perturbingxt by25 anyucannot substantially reduce the cumulative loss.Hence, itcan besaid that the26 sequence {x1,,xT} is asymptotically calibrated with respect to{f1,,fT} if:27 Weindeedranexperiments usingSGDwithmomentum forvariousdecayparameters andconcluded thatSGDwith36 momentum is not even as stable as SGD-online (standard SGD without momentum) as shown in Figure 1.