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Towards Estimating Bounds on the Effect of Policies under Unobserved Confounding
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Derives graphical criteria and analytical bounds on the effect of stochastic/conditional policies under unobserved confounding, and a double-machine-learning estimator for those bounds from finite samples.
Problem
Policy effects are often not identifiable under unobserved confounding; existing bounds mostly cover atomic interventions and discrete small systems, and no scalable estimators exist for bounds with continuous outcomes and high-dimensional covariates.
Approach
Uses partial adjustment sets and partial conditional instrumental sets, read from the causal diagram via d-separation in manipulated graphs, to tighten natural policy bounds; an algorithm assembles these into bounds, and DML estimators with nuisance functions estimate them with robustness to misspecification.
Key results
- Graphical criteria (partial adjustment and partial instrumental sets) yield bounds tighter than natural policy bounds, with the combined Alg. 1 giving the narrowest width in simulations.
- The DML estimator is robust to misspecification of either nuisance (unbiased under misspecification per Prop. 9) and converges faster than competing estimators when nuisances have noise decaying as n^-1/4.
- In the obesity case study, policies promoting healthier lifestyles (alpha 0.2 to 0.8) are associated with lower expected BMI bounds, but substantial uncertainty remains.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the DML estimator instead of the probability-weighting or regression estimator under nuisance misspecification | Policy-effect bound estimation · Synthetic simulations, Settings 2 and 3 | absolute average error (AAE) | Helped |
| Use the DML estimator instead of competing estimators when nuisance estimates contain decaying noise | Policy-effect bound estimation · Synthetic simulations, Setting 4 | absolute average error (AAE) | Helped |
| Use the DML estimator with high-dimensional adjustment variables W | Policy-effect bound estimation · Synthetic simulations, high-dimensional partial adjustment set | absolute average error (AAE) | Helped |
| Increase the dataset size | Proposed estimators T PW, T REG, and T DML · Synthetic simulations, all data-generating mechanisms | absolute average error (AAE) | Helped |
| Use partial adjustment and partial instrumental-set criteria together instead of the natural policy bounds alone | Policy-effect bounds · Synthetic simulations, bound-width evaluation | bound width | Helped |
| Increase the health campaign policy probability α | Health campaign policy on high-calorie food intake and exercise · Colombia, Peru, and Mexico health campaign evaluation | expected BMI | Helped |
Surprising findings
- The authors conjecture that finding an optimal analytical bound from the graph alone is undecidable.
- Natural policy bounds are tight in general, so no better bound exists for the example policy without further graph structure.
Limitations
- Assumes a known causal diagram; d-separation assumptions must be justified by domain knowledge.
- Estimation results are asymptotic; finite-sample uncertainty is not quantified.
- Bounds can be wide and depend on the data distribution, so they may not be informative in practice.
Experimental setup
Datasets: synthetic simulations obesity lifestyle survey data from Colombia, Peru and Mexico
Benchmarks: synthetic simulations with four data generating mechanisms obesity health campaign data
Metrics: absolute average error bound width
Baselines: natural policy bounds T_PW T_REG
Builds on: Manski bounds natural bounds (Robins) double machine learning sigma-calculus Balke and Pearl bounds
Closest papers by meaning
- Model-Free and Model-Based Policy Evaluation when Causality is Uncertain (ICML 2021 · similarity 0.91)
- Towards Safe Policy Learning under Partial Identifiability: A Causal Approach (AAAI 2024 · similarity 0.88)
- Efficient Policy Evaluation Across Multiple Different Experimental Datasets (NeurIPS 2024 · similarity 0.88)
- Off-policy Evaluation Beyond Overlap: Sharp Partial Identification Under Smoothness (ICML 2024 · similarity 0.87)
- Predictive Performance Comparison of Decision Policies Under Confounding (ICML 2024 · similarity 0.86)
- Learning Representations of Instruments for Partial Identification of Treatment Effects (ICML 2025 · similarity 0.86)
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