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Learning Decision Policies with Instrumental Variables through Double Machine Learning
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Proposes DML-IV, a double/debiased machine learning approach with a Neyman-orthogonal score for DNN-based instrumental variable regression, yielding N^{-1/2} convergence and suboptimality bounds for offline IV bandit policies.
Problem
Learning causal functions and decision policies from confounded offline data using instrumental variables with deep neural networks, where two-stage DNN IV regression suffers regularisation and overfitting bias.
Approach
Derives a Neyman-orthogonal score for two-stage IV regression by replacing the outcome R with a learned conditional expectation s(c,z), and trains the second stage with K-fold cross-fitting so that DNN nuisance estimators can converge at N^{-1/2} rate.
Key results
- DML-IV achieves lower MSE than Deep IV, DeepGMM, KIV and DFIV across dataset sizes on the aeroplane ticket demand benchmark (20 runs, median and quartiles).
- In the high-dimensional MNIST setting, DML-IV consistently learns near-optimal pricing policies with only 2000 samples, while standard offline bandit methods fail to beat a random policy.
- Theory gives O(N^{-1/2}) convergence of the DML-IV estimator and O(N^{-1/2}) suboptimality bounds for the induced policy with high probability.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DML-IV instead of competing IV regression methods | IV regression · Aeroplane ticket demand, low-dimensional context | MSE | Helped |
| Use DML-IV instead of competing IV regression methods | IV regression · Aeroplane ticket demand, MNIST high-dimensional context | MSE | Helped |
| Use DML-IV instead of competing IV regression methods | Offline IV bandit · Aeroplane ticket demand, low-dimensional context | average reward | Helped |
| Use DML-IV instead of competing IV regression methods | Offline IV bandit · Aeroplane ticket demand, MNIST high-dimensional context | average reward | Helped |
| Use DML-IV instead of competing IV regression methods | Semi-synthetic real-world datasets · IHDP and PM-CMR | average reward | Helped |
| Remove K-fold cross-fitting and train nuisance models once on the full dataset (CE-DML-IV) (ablation) | DML-IV · Low-dimensional datasets | MSE | No clear effect |
| Remove K-fold cross-fitting and train nuisance models once on the full dataset (CE-DML-IV) (ablation) | DML-IV · Aeroplane ticket demand, MNIST high-dimensional context | average reward | Hurt |
| Remove K-fold cross-fitting and train nuisance models once on the full dataset (CE-DML-IV) (ablation) | DML-IV · Semi-synthetic real-world datasets IHDP and PM-CMR | MSE | No clear effect |
| Remove K-fold cross-fitting and train nuisance models once on the full dataset (CE-DML-IV) (ablation) | DML-IV · Semi-synthetic real-world datasets IHDP and PM-CMR | average reward | No clear effect |
| Use offline bandit algorithms that do not explicitly exploit IVs instead of an IV-aware policy method | Offline IV bandit · Aeroplane ticket demand, low-dimensional context | average reward | Hurt |
Surprising findings
- Standard offline bandit algorithms (PEVI, LinLCB, NeuraLCB, etc.) that ignore instruments fail to outperform a random policy on confounded data.
- The computationally cheaper CE-DML-IV without cross-fitting matches DML-IV on low-dimensional datasets.
Limitations
- Theoretical guarantees require finite-dimensional parameterised h and nuisance effective dimension d_N=o(N^{1/4}), and identifiability assumptions.
- Cross-fitting with K=10 folds is computationally expensive; CE-DML-IV lacks convergence guarantees.
- Weak-instrument behaviour is only evaluated empirically, with no theory for non-linear IV models.
Experimental setup
Datasets: aeroplane ticket demand (synthetic) MNIST IHDP PM-CMR
Benchmarks: aeroplane ticket demand dataset IHDP PM-CMR MNIST-based high-dimensional ticket demand
Metrics: mean squared error of estimated causal function average reward of induced policy
Baselines: Deep IV DeepGMM KIV DFIV PEVI LinLCB NeuraLCB KernLCB NeuralLinLCB NeuralLinGreedy
Builds on: double/debiased machine learning two-stage least squares Deep IV DeepGMM DFIV
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