Double Distributionally Robust Bid Shading for First Price Auctions

TL;DR

This work provides a max-min formulation in which the two ambiguity sets are essential to adjusting the shape of the bid-shading policy in a principled way so as to effectively cope with uncertainty and is efficient to compute and systematically outperforms its non-robust counterpart on real datasets provided by Yahoo DSP.

Abstract

Bid shading has become a standard practice in the digital advertising industry, in which most auctions for advertising (ad) opportunities are now of first price type. Given an ad opportunity, performing bid shading requires estimating not only the value of the opportunity but also the distribution of the highest bid from competitors (i.e. the competitive landscape). Since these two estimates tend to be very noisy in practice, first-price auction participants need a bid shading policy that is robust against relatively significant estimation errors. In this work, we provide a max-min formulation in which we maximize the surplus against an adversary that chooses a distribution both for the value and the competitive landscape, each from a Kullback-Leibler-based ambiguity set. As we demonstrate, the two ambiguity sets are essential to adjusting the shape of the bid-shading policy in a principled way so as to effectively cope with uncertainty. Our distributionally robust bid shading policy is efficient to compute and systematically outperforms its non-robust counterpart on real datasets provided by Yahoo DSP.

Figures (4)

• Figure 1: Real-time bidding system for first-price auction
• Figure 2: Surplus change
• Figure 3: Spend difference
• Figure 4: Difference in wins in the largest 15 lines (D: DRBS, B: baseline)

Theorems & Definitions (5)

• Theorem 1
• Corollary 1
• Proposition 1
• proof : Proof of Theorem \ref{['main']}
• proof : Proof of Proposition \ref{['prop']}