Given an algorithmic predictor that is accurate on some source population consisting of strategic human decision subjects, will it remain accurate if the population respond to it? In our setting, an agent or a user corresponds to a sample $(X,Y)$ drawn from a distribution $\cal{D}$ and will face a model $h$ and its classification result $h(X)$. Agents can modify $X$ to adapt to $h$, which will incur a distribution shift on $(X,Y)$. Our formulation is motivated by applications where the deployed machine learning models are subjected to human agents, and will ultimately face responsive and interactive data distributions. We formalize the discussions of the transferability of a model by studying how the performance of the model trained on the available source distribution (data) would translate to the performance on its induced domain. We provide both upper bounds for the performance gap due to the induced domain shift, as well as lower bounds for the trade-offs that a classifier has to suffer on either the source training distribution or the induced target distribution. We provide further instantiated analysis for two popular domain adaptation settings, including covariate shift and target shift.

翻译：给定一个在由战略型人类决策主体构成的源群体上表现准确的算法预测器，当该群体对其产生响应时，该预测器是否仍能保持准确？在我们的设定中，智能体或用户对应从分布 $\cal{D}$ 中抽取的样本 $(X,Y)$，将面对模型 $h$ 及其分类结果 $h(X)$。智能体可通过修改 $X$ 来适应 $h$，这会导致 $(X,Y)$ 的分布偏移。该设定受实际应用场景驱动——当部署的机器学习模型面向人类智能体时，最终将面临响应式且交互式数据分布。我们通过研究基于可用源分布（数据）训练的模型性能如何转化为其在诱导领域上的表现，形式化探讨了模型可迁移性问题。我们不仅给出了由诱导领域偏移导致的性能差距的上界，还提供了分类器在源训练分布与诱导目标分布之间必须承受的权衡下界。我们进一步针对两种流行的领域自适应场景（包括协变量偏移与目标偏移）进行了实例化分析。