A Calibration of the parameters

We only prove the calibration in the setting of linear regression with square loss (i.e., for Theorem 3 only and not for the general Theorem 1). It remains an open question whether the calibration of the parameters can be performed in the general setting of Section 3. We leave this question for future research. Furthermore, for the sake of clarity the adaption to Y (which is only necessary for clipping) is not considered here. However, it can be achieved simultaneously by updating the clipping range based on the past observations Ys, s ! t− 1 (see Gerchinovitz, 2013, Section 4.5).