预测-干预博弈与不变集：基于稳定覆盖集的因果预测研究
Prediction-Intervention Games and Invariant Sets
AI 导读
这篇 arXiv 论文研究一类 Stackelberg 博弈：领导者基于观测数据选择预测函数，跟随者随后对结构因果模型中的协变量进行干预以最大化自身目标。作者证明，对两类常见跟随者目标，基于不变子集“稳定覆盖集”的预测不劣于基于因果父变量的预测，并给出稳定覆盖集预测在最坏情况干预下最优的充分条件，辅以模拟和真实数据实验验证。
正文 · 原文
Abstract:We consider the following two-player game: using observational data, the leader chooses a prediction function for a response variable $Y$ from given covariates. The follower then reacts with an intervention on some covariates in the underlying structural causal model to maximize their own objective. The leader knows the intervention targets, but may have limited knowledge of the follower's objective. We call this setup a prediction-intervention game, a special case of a Stackelberg game. Finding an optimal strategy for the leader is generally difficult. To avoid severe performance loss, the leader may base their prediction on the causal parents of $Y$, or more generally on an invariant subset of covariates. We prove, for two common classes of follower objectives, that predictors based on the stable blanket, an invariant subset, are at least as good as those based on the causal parents. We further upper bound the leader's post-intervention risk by a worst-case risk over allowed interventions and strengthen existing distribution generalization results to analyze this bound: we give sufficient conditions under which stable-blanket predictors are worst-case optimal, and show by examples that these conditions cannot in general be dropped. Finally, we discuss practical strategies for settings with known and unknown graph, and test them on simulated and real-world data.
| Subjects: | Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Methodology (stat.ME) |
| Cite as: | arXiv:2605.16828 [stat.ML] |
| (or arXiv:2605.16828v2 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2605.16828 arXiv-issued DOI via DataCite |
Submission history
From: Linus Kühne [view email]
[v1]
Sat, 16 May 2026 06:15:41 UTC (4,192 KB)
[v2]
Wed, 4 Nov 2026 13:54:16 UTC (4,223 KB)
来源：arXiv cs.AI · arxiv.org