Reach Measurement, Optimization and Frequency Capping In Targeted Online Advertising Under k-Anonymity

TL;DR

The paper tackles reach measurement and optimization in targeted online advertising under the $k$-anonymous privacy protocol, where individual user tracking is replaced by group-level information. It derives exact and streaming formulas for the expected reach under frequency caps, including extensions to non-uniform within-group behavior, and proposes probabilistic discounting to optimize campaigns with group-based impressions. A complete framework is provided for estimating reach probability $p_t$ and solving the impression-bidding problem under privacy constraints via a Lagrangian formulation, with practical online solvers. Through Monte Carlo simulations and real-world data, the work quantifies the privacy–efficiency tradeoff, showing a measurable decline in performance as privacy increases but highlighting feasible privacy gains at modest costs. Overall, the study advances understanding of privacy-preserving reach measurement and optimization, and suggests that relaxing uniformity within groups can substantially improve performance while maintaining $k$-anonymity.

Abstract

The growth in the use of online advertising to foster brand awareness over recent years is largely attributable to the ubiquity of social media. One pivotal technology contributing to the success of online brand advertising is frequency capping, a mechanism that enables marketers to control the number of times an ad is shown to a specific user. However, the very foundation of this technology is being scrutinized as the industry gravitates towards advertising solutions that prioritize user privacy. This paper delves into the issue of reach measurement and optimization within the context of $k$-anonymity, a privacy-preserving model gaining traction across major online advertising platforms. We outline how to report reach within this new privacy landscape and demonstrate how probabilistic discounting, a probabilistic adaptation of traditional frequency capping, can be employed to optimize campaign performance. Experiments are performed to assess the trade-off between user privacy and the efficacy of online brand advertising. Notably, we discern a significant dip in performance as long as privacy is introduced, yet this comes with a limited additional cost for advertising platforms to offer their users more privacy.

Figures (6)

• Figure 1: Illustration of the k-anonymous Privacy Protocol, highlighting the process from user visit to ad display within the framework of $k$-anonymity.
• Figure 2: Experiments on reach measurement. Reach is defined as the number of impressions under the frequency cap. A: Distribution of reach with 250 impressions and a frequency cap of 3. The black dashed vertical line indicates the mean of the sampled distribution. The red solid line depicts the expected reach calculated from Theorem \ref{['thm:measurement']}. B: Distributions of reach under different numbers of impressions. C: Variance of reach with different group sizes.
• Figure 3: Privacy vs. efficiency in online brand advertising. The relative ROAS is plotted against different group sizes $k$ representing different levels of user privacy.
• Figure 4: Relative frequency of each user within a group. Distributions of six groups are shown. Users are ranked based on their frequency.
• Figure 5: Reach measurement performance comparison. The error metric of each campaign is plotted as a dot. Error bars represent standard deviation. A, B, C, D represents the four approaches listed in section \ref{['sec:realworld']}.

Theorems & Definitions (11)

• Theorem 1: Reach in Expectation
• Corollary 1
• Corollary 2
• Lemma 1: Covariance
• Theorem 2: Concentration Bounds
• Theorem 3: Over-exposed Users
• Theorem 4
• Corollary 3
• Theorem 5: Probability of Additional Reach
• Corollary 4