Hi Dirk,
Thanks for your interests in this article, and thanks for pointing out where I may mislead the readers.
In fact, to calculate the bias term, we simply use this closest training sample's cross-validation error AS the prediction bias. There is no interpolation or other forms of approximation. Although simple, we found this practice sufficient for our active learning purposes.
Of course, the more accurate "estimation" of the bias term, the more effective and faster convergence this prediction-error based learning strategy will be. In that sense, perhaps performing some kind of interpolation rather than simply treating them (x_i and x*) as equal may yield better results.
I've removed "approximation" in the original text to avoid any confusion.
Thank you again!