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Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments
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Derives partial-identification bounds for CATE from multi-environment observational data by treating environment as an instrumental variable, and proposes model-agnostic meta-learners (WB and CB variants) to estimate these bounds.
Problem
CATE estimation from observational data collected across multiple environments when overlap and unconfoundedness may be violated, so point identification fails.
Approach
Interprets the environment indicator as a discrete instrumental variable, generalizes natural IV bounds (Manski-style with propensity scores) to CATE using propensity differences across environments, and develops two-stage pseudo-outcome meta-learners (plug-in, RA, IPW, DR) to estimate the tightest bounds.
Key results
- On synthetic data, CB-IPW achieved the lowest RMSE on dataset 1 (0.117 ± 0.057), while CB-DR was best on dataset 2 (0.111 ± 0.069).
- Naive plug-in learner had lower RMSE for within-environment bounds (0.073 and 0.075) than the two-stage WB learner (0.142 and 0.130), so two-stage learners were not uniformly better.
- On the COVID-19 Brazil case study, cross-environment bounds tightened the estimated bounds, and the two-stage learners gave results similar to the naive plug-in learner.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CB-IPW instead of the other evaluated learners | Bound estimation · Synthetic Data 1 | RMSE: 0.117 ± 0.057 | Helped |
| Use CB-DR instead of the other evaluated learners | Bound estimation · Synthetic Data 2 | RMSE: 0.111 ± 0.069 | Helped |
| Use two-stage cross-environment learners rather than the naïve plug-in learner | Cross-environment bound estimation · Synthetic Data 1 and Synthetic Data 2 | RMSE | Mixed |
| Use two-stage WB-learner with CB-DR rather than the naïve plug-in learner | Bound estimation · Synthetic Data 2 | RMSE | Helped |
| Use cross-environment bounds rather than within-environment bounds | Tightest bound estimation · Synthetic and real-world data | bound tightness | Helped |
Surprising findings
- Violations of overlap can increase bound tightness when treatment assignment differs sufficiently across environments.
- Within-environment bounds were not helpful; almost only cross-environment bounds gave the tightest bounds.
Limitations
- Requires the environment to act as an instrument (no correlation with unobserved confounders), which cannot be tested.
- Experiments are a proof-of-demonstration with simple MLPs and only 5 runs; no broad benchmarking.
- Real-world case study lacks ground-truth CATE so performance cannot be verified.
Experimental setup
Datasets: Synthetic dataset 1 Synthetic dataset 2 COVID-19 hospitalizations in Brazil
Benchmarks: Synthetic dataset 1 Synthetic dataset 2 COVID-19 Brazil case study
Metrics: RMSE to oracle bounds
Baselines: naive plug-in learner WB naive CB naive CB-PI CB-RA CB-IPW CB-DR
Builds on: natural bounds for IV with discrete variables Manski bounds DR-learner X-learner CATENets
Closest papers by meaning
- Learning Representations of Instruments for Partial Identification of Treatment Effects (ICML 2025 · similarity 0.92)
- A Non-parametric Direct Learning Approach to Heterogeneous Treatment Effect Estimation under Unmeasured Confounding (NeurIPS 2024 · similarity 0.90)
- Model-agnostic meta-learners for estimating heterogeneous treatment effects over time (ICLR 2025 · similarity 0.90)
- Estimating Heterogeneous Treatment Effects by Combining Weak Instruments and Observational Data (NeurIPS 2024 · similarity 0.90)
- AutoCATE: End-to-End, Automated Treatment Effect Estimation (ICML 2025 · similarity 0.89)
- A Meta-learner for Heterogeneous Effects in Difference-in-Differences (ICML 2025 · similarity 0.89)
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