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Prediction-Intervention Games and Invariant Sets

NeurIPS 2026 · Probabilistic and scientific modeling › Causal discovery · approach: Causal approaches to fairness · 0 citations (OpenAlex)

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Introduces prediction-intervention games (leader predicts, strategic follower intervenes in an SCM) and shows stable-blanket predictors weakly dominate parent-based ones for two follower-utility classes, with worst-case optimality conditions and stabilized classification experiments.

Problem

A leader chooses a predictor for Y from covariates, but a strategic follower then intervenes on covariates in the SCM to maximize its own objective, so the test distribution depends on the predictor; the leader needs a predictor robust to these follower-induced shifts without knowing the follower's

Approach

Formalizes the leader-follower game in a causal (SCM) setting and shows predictors based on the stable blanket (an invariant subset that includes non-intervened children of Y) are never worse than parent-based predictors for two common follower utilities; bounds post-intervention risk by worst-case risk over allowed interventions and gives sufficient conditions for stable-blanket worst-case optima

Key results

• On synthetic linear-Gaussian SCM, the stable-blanket predictor has constant deployment MSE and is uniformly better than the parent predictor, while the all-variable predictor's MSE rises sharply with intervention bound.
• On Causal Chambers, only the all-variables predictor lets the follower improve its objective; stabilized classification selects {RGB, ir_2, vis_2} and matches the best invariant predictor.

Surprising findings

• Under 0-1 loss, IRM can accept a representation that is not conditionally invariant, leading to worse worst-case accuracy than a subset-based invariant predictor.
• A predictor using no stable-blanket information can beat all invariant-subset predictors in worst-case risk when the strong-intervention graphical condition fails (Brier score example with SB(Y) empty).

Limitations

• Results rely on strong-intervention assumptions which may not hold in practice.
• Finite-sample estimation errors can be exploited by the follower; finite-sample analysis left for future work.
• Solving prediction-intervention games in general is presumed hard and not addressed.

Experimental setup

Datasets: synthetic linear-Gaussian SCM synthetic nonlinear SCM Causal Chambers light tunnel

Benchmarks: synthetic prediction-intervention games Causal Chambers light tunnel

Metrics: MSE follower objective improvement 95% confidence intervals over 10 runs

Baselines: parent-based predictor all-variable predictor invariant most-predictive (IMP) stabilized regression

Builds on: invariant causal prediction stable blanket stabilized regression strategic classification anchor regression

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