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Efficient Adaptive Experimentation with Noncompliance
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Derives the semiparametric efficiency bound for ATE estimation under adaptive instrument assignment with noncompliance, and proposes AMRIV, an adaptive multiply robust IV estimator with variance-optimal instrument allocation and anytime-valid asymptotic confidence sequences.
Problem
Estimating the average treatment effect in sequential experiments where only a binary instrument (encouragement) can be assigned adaptively and treatment uptake is endogenous (noncompliance).
Approach
Derives the efficiency bound under history-dependent instrument policies, shows the optimal policy allocates instruments proportional to the square root of residual variance (combining outcome and compliance noise), and pairs this online policy with a sequential recentered efficient-influence-function (MRIV-style) estimator that attains the bound with multiply robust consistency.
Key results
- AMRIV approaches the oracle efficiency benchmark under adaptive assignment while AMRIV-NA shows a constant efficiency gap (synthetic study, T=2000).
- Only AMRIV and AMRIV-NA achieve nominal 95% coverage; A2IPW is biased and fails to converge due to unaddressed confounding, and DM-MS diverges under misspecified delta(X).
- AMRIV-MS remains consistent under misspecification of delta(X), reflecting the multiply robust property.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use adaptive variance-aware instrument assignment instead of uniform random assignment | AMRIV · Synthetic one-sided noncompliance | normalized MSE | Helped |
| use adaptive variance-aware instrument assignment instead of uniform random assignment | AMRIV · Synthetic one-sided noncompliance | MSE | Helped |
| use adaptive variance-aware instrument assignment instead of uniform random assignment | AMRIV · TripAdvisor semi-synthetic data | efficiency | Helped |
| use AMRIV rather than A2IPW | ATE estimation · Synthetic one-sided noncompliance | consistency | Helped |
| deliberately misspecify the δ(X) estimator (ablation) | AMRIV · Synthetic one-sided noncompliance | consistency | No clear effect |
| deliberately misspecify the δ(X) estimator (ablation) | DM · Synthetic one-sided noncompliance | consistency | Hurt |
| use AMRIV or AMRIV-NA rather than the other evaluated methods | ATE estimation · Synthetic one-sided noncompliance | 95% confidence interval coverage | Helped |
| use misspecified or plug-in methods rather than AMRIV | ATE estimation · Synthetic one-sided noncompliance | 95% confidence interval coverage | Hurt |
| use adaptive instrument assignment with AMRIV | AMRIV · TripAdvisor semi-synthetic data | consistency | Helped |
Surprising findings
- Under low compliance the optimal policy shifts toward uniform allocation rather than Neyman allocation, assigning more units to Z=1 to offset scarce treatment uptake.
Limitations
- Asymptotic rather than finite-sample guarantees; confidence sequences are asymptotic and valid only after a burn-in period.
- Requires bounded outcomes and nuisance estimates and identification assumption (unconfounded compliance) that may fail in practice.
- Efficiency results rely on L2-consistent nuisance estimates with truncation schedule k_t growing with t.
Experimental setup
Datasets: synthetic one-sided noncompliance environment TripAdvisor customer simulator (semi-synthetic)
Benchmarks: synthetic simulation (T=2000, 1000 trajectories) semi-synthetic TripAdvisor simulator
Metrics: normalized MSE relative to oracle MSE empirical 95% CI coverage
Baselines: AMRIV-NA DM DM-NA A2IPW Oracle Oracle-NA AMRIV-MS DM-MS
Builds on: MRIV A2IPW Neyman allocation cross-fitting
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