  We study the design of loss functions for click-through rates (CTR) to
optimize (social) welfare in advertising auctions. Existing works either only
focus on CTR predictions without consideration of business objectives (e.g.,
welfare) in auctions or assume that the distribution over the participants'
expected cost-per-impression (eCPM) is known a priori, then use various
additional assumptions on the parametric form of the distribution to derive
loss functions for predicting CTRs. In this work, we bring back the welfare
objectives of ad auctions into CTR predictions and propose a novel weighted
rankloss to train the CTR model. Compared to existing literature, our approach
provides a provable guarantee on welfare but without assumptions on the eCPMs'
distribution while also avoiding the intractability of naively applying
existing learning-to-rank methods. Further, we propose a theoretically
justifiable technique for calibrating the losses using labels generated from a
teacher network, only assuming that the teacher network has bounded $\ell_2$
generalization error. Finally, we demonstrate the advantages of the proposed
loss on synthetic and real-world data.
