Generalization Error Bounds for Learning under Censored Feedback
Yifan Yang Ali Payani Parinaz Naghizadeh
Generalization error bounds from learning theory provide statistical
guarantees on how well an algorithm will perform on previously unseen data. In
this paper, we characterize the impacts of data non-IIDness due to censored
feedback (a.k.a. selective labeling bias) on such bounds. We first derive an
extension of the well-known Dvoretzky-Kiefer-Wolfowitz (DKW) inequality, which
characterizes the gap between empirical and theoretical CDFs given IID data, to
problems with non-IID data due to censored feedback. We then use this CDF error
bound to provide a bound on the generalization error guarantees of a classifier
trained on such non-IID data. We show that existing generalization error bounds
(which do not account for censored feedback) fail to correctly capture the
model's generalization guarantees, verifying the need for our bounds. We
further analyze the effectiveness of (pure and bounded) exploration techniques,
proposed by recent literature as a way to alleviate censored feedback, on
improving our error bounds. Together, our findings illustrate how a decision
maker should account for the trade-off between strengthening the generalization
guarantees of an algorithm and the costs incurred in data collection when
future data availability is limited by censored feedback.