Multiplicative Bidding in Online Advertising

TL;DR

This paper studies the multiplicative bidding language used in online advertising, analyzing its optimization challenges, providing algorithms and hardness results, and validating their effectiveness with real data experiments.

Contribution

It introduces the foundational optimization problem for multiplicative bidding, offers approximation algorithms and hardness results, and empirically validates the approach with real-world data.

Findings

An $O(\log n)$-approximation algorithm for multiplicative prices and monotone values.

Hardness results matching information-theoretic bounds.

Algorithms perform favorably against baselines on real data.

Abstract

In this paper, we initiate the study of the multiplicative bidding language adopted by major Internet search companies. In multiplicative bidding, the effective bid on a particular search auction is the product of a base bid and bid adjustments that are dependent on features of the search (for example, the geographic location of the user, or the platform on which the search is conducted). We consider the task faced by the advertiser when setting these bid adjustments, and establish a foundational optimization problem that captures the core difficulty of bidding under this language. We give matching algorithmic and approximation hardness results for this problem; these results are against an information-theoretic bound, and thus have implications on the power of the multiplicative bidding language itself. Inspired by empirical studies of search engine price data, we then codify the relevant restrictions of the problem, and give further algorithmic and hardness results. Our main technical contribution is an $O(\log n)$-approximation for the case of multiplicative prices and monotone values. We also provide empirical validations of our problem restrictions, and test our algorithms on real data against natural benchmarks. Our experiments show that they perform favorably compared with the baseline.