[论文解读] The Role of Randomness and Noise in Strategic Classification

Mark Braverman, Sumegha Garg|arXiv (Cornell University)|May 17, 2020

Auction Theory and Applications参考文献 18被引用 7

一句话总结

本文表明，在个体通过操纵特征以获得有利结果的战略分类场景中，随机分类器和噪声特征信号能够同时提升准确率与公平性。研究发现，即使分类器本身无需随机化，引入噪声或随机性也能通过降低策略性操纵成本并稳定结果，实现优于确定性分类器的均衡结果。

ABSTRACT

We investigate the problem of designing optimal classifiers in the strategic classification setting, where the classification is part of a game in which players can modify their features to attain a favorable classification outcome (while incurring some cost). Previously, the problem has been considered from a learning-theoretic perspective and from the algorithmic fairness perspective. Our main contributions include 1. Showing that if the objective is to maximize the efficiency of the classification process (defined as the accuracy of the outcome minus the sunk cost of the qualified players manipulating their features to gain a better outcome), then using randomized classifiers (that is, ones where the probability of a given feature vector to be accepted by the classifier is strictly between 0 and 1) is necessary. 2. Showing that in many natural cases, the imposed optimal solution (in terms of efficiency) has the structure where players never change their feature vectors (the randomized classifier is structured in a way, such that the gain in the probability of being classified as a 1 does not justify the expense of changing one's features). 3. Observing that the randomized classification is not a stable best-response from the classifier's viewpoint, and that the classifier doesn't benefit from randomized classifiers without creating instability in the system. 4. Showing that in some cases, a noisier signal leads to better equilibria outcomes -- improving both accuracy and fairness when more than one subpopulation with different feature adjustment costs are involved. This is interesting from a policy perspective, since it is hard to force institutions to stick to a particular randomized classification strategy (especially in a context of a market with multiple classifiers), but it is possible to alter the information environment to make the feature signals inherently noisier.

研究动机与目标

• 研究随机性与噪声如何影响战略分类中分类器的效率，其中个体通过操纵特征以获得更好结果。
• 分析在斯塔克尔贝格博弈设定下，随机分类器是否能实现高于确定性分类器的效率（准确率减去操纵成本）
• 从分类器的视角分析随机分类器的稳定性，并评估其实际可行性
• 研究噪声信号如何作为承诺机制，在多子群体设定中提升公平性与准确率

提出的方法

• 为分配每个特征向量概率值（取值范围为[0,1]）的随机分类器形式化定义了斯塔克尔贝格均衡
• 将效率定义为分类准确率减去合格个体所承担的总操纵成本
• 采用基于阈值的分类器，并将特征操纵成本建模为与合格阈值距离的函数
• 引入噪声信号模型，其中特征受均值为0、标准差为σ的高斯噪声污染，并与无噪声私有信号设定下的结果进行比较
• 分析具有不同操纵成本但相同资格标准的子群体，以隔离公平性与准确率的影响
• 采用数学优化方法比较无噪声与有噪声特征设定下的效用（准确率），证明噪声可改善结果

实验结果

研究问题

• RQ1 在战略分类中，随机分类器是否能实现高于确定性分类器的效率？
• RQ2 是否存在一种情形，即在特征中增加噪声可带来比使用无噪声信号更高的分类准确率与公平性？
• RQ3 为何分类器可能更倾向于选择噪声特征而非精确特征，即使后者可用？
• RQ4 从分类器视角出发，随机分类器在何种条件下不稳定，这对实际部署有何影响？
• RQ5 特征中的噪声是否可作为改善战略分类系统整体结果的承诺机制？

主要发现

• 存在某些情形下，具有标准差σ的高斯噪声特征信号可实现严格高于无噪声私有信号的分类准确率，即使子群体具有相同的资格标准
• 在噪声特征下，最优分类器可实现高于无噪声特征下（U(fσ*) > U(f0*)）的效用，具体示例显示当σB = σ且σA = 0.1σ时存在此改进
• 在子群体规模不均且操纵成本不同的情况下，噪声特征可同时提升公平性与准确率，即使在无噪声设定下系统已具备公平性
• 在性能上优于确定性分类器的随机分类器，通常从分类器视角来看是不稳定的，因此在多分类器市场中难以实际部署
• 特征中的噪声可作为强制随机化的实用替代方案，在无需分类器承诺采用随机策略的前提下，提升系统效率
• 使用噪声信号可通过降低操纵动机，带来更优的均衡结果，尤其当不同子群体面临不同的特征修改成本时