[论文解读] Fairness in ad auctions through inverse proportionality.

Shuchi Chawla, Meena Jagadeesan|arXiv (Cornell University)|Mar 31, 2020

Auction Theory and Applications参考文献 7被引用 8

一句话总结

本文提出逆比例分配（Inverse Proportional Allocation），一种用于广告拍卖的 truthful（诚实）、无先验（prior-free）拍卖机制，通过价值稳定性确保个体公平性——即相似用户获得相似的广告分配。该机制实现了与广告商数量无关的最优社会福利的常数因子近似，显著优于以往工作。

ABSTRACT

We study the tradeoff between social welfare maximization and in the context of ad auctions. We study an ad auction setting where users arrive one at a time, $k$ advertisers submit values for each user, and the auction assigns a distribution over ads to each user. Following the works of Dwork and Ilvento (2019) and Chawla et al. (2020), our goal is to design a truthful auction that satisfies individual fairness in its outcomes: informally speaking, users that are similar to each other should obtain similar allocations of ads. We express the constraint as a kind of stability condition: any two users that are assigned multiplicatively similar values by all the advertisers must receive additively similar allocations for each advertiser. This value stability constraint is expressed as a function that maps the multiplicative distance between value vectors to the maximum allowable $\ell_\infty$ distance between the corresponding allocations. Standard auctions do not satisfy this kind of value stability. Our main contribution is a new class of allocation algorithms called Inverse Proportional Allocation that achieve value stability with respect to an expressive class of stability conditions. These allocation algorithms are truthful and prior-free, and achieve a constant factor approximation to the optimal (unconstrained) social welfare. In particular, the approximation ratio is independent of the number of advertisers in the system. In this respect, these allocation algorithms greatly surpass the guarantees achieved in previous work. In fact, our algorithms achieve a near optimal tradeoff between and social welfare under a mild assumption on the value stability constraint. We also extend our results to broader notions of that we call subset fairness.

研究动机与目标

• 设计一种 truthful 广告拍卖机制，通过确保相似用户获得相似广告分配来实现个体公平性。
• 将公平性形式化为价值稳定性约束：乘法上相似的广告商估值必须导致加法上相似的分配结果。
• 开发满足此稳定性条件的同时保持高社会福利的分配算法。
• 实现与广告商数量无关的最优社会福利的常数因子近似。
• 将公平性框架扩展至更广泛的范畴，如子集公平性（subset fairness）

提出的方法

• 提出一类新型分配算法，称为逆比例分配，通过将广告商估值与分配结果成反比关系，以确保价值稳定性。
• 定义一个稳定性函数，将估值向量之间的乘法距离映射为分配结果之间允许的最大 ℓ∞ 距离。
• 设计分配规则，使其在所有估值相近的用户对之间均满足价值稳定性约束。
• 通过构建分配规则，使竞标者无法通过虚报估值获益，从而确保机制的诚实性。
• 采用无先验设计，即无需知晓广告商估值的分布信息。
• 通过将稳定性条件推广至用户群体，将框架扩展至子集公平性。

实验结果

研究问题

• RQ1 如何设计一种 truthful 广告拍卖机制，以在动态用户到达场景下通过价值稳定性实现个体公平性？
• RQ2 在价值稳定性约束下，广告拍卖中社会福利与公平性之间的最佳权衡是什么？
• RQ3 我们能否实现与广告商数量无关的最优社会福利的常数因子近似？
• RQ4 公平性框架如何从个体公平性扩展至子集公平性？

主要发现

• 所提出的逆比例分配机制对一类表达性强的稳定性函数满足价值稳定性约束。
• 该机制具有 truthful 性质且为无先验设计，无需对广告商估值的分布做出假设。
• 其可实现与广告商数量无关的最优社会福利的常数因子近似。
• 在对价值稳定性约束施加温和假设的前提下，该近似比接近最优。
• 通过将稳定性条件推广至用户群体，该框架可扩展以实现子集公平性。