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Stronger Neyman Regret Guarantees for Adaptive Experimental Design
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Modifies ClipOGD for adaptive IPW ATE experiments to get anytime O~(log T) Neyman regret under strengthened outcome bounds, and proposes MGATE, a sleeping-experts multigroup design achieving O~(sqrt T) multigroup Neyman regret for overlapping covariate groups.
Problem
Adaptive sequential randomized experiments for unbiased ATE estimation in the finite-population (design-based) potential outcomes setting need low-variance IPW estimates, measured by Neyman regret relative to the best nonadaptive Bernoulli design, including for subgroups defined by pre-treatment cov
Approach
Use a strongly convex analysis of the Neyman objective under a stricter outcome lower bound to get a decreasing 1/t learning rate for clipped OGD (ClipOGD^SC), yielding log T regret; for covariate groups, aggregate per-group ClipOGD-style designs with a scale-free sleeping-experts algorithm (MGATE) to get multigroup regret guarantees for arbitrary overlapping groups.
Key results
- ClipOGD^SC achieves anytime O~(log T) Neyman regret under the stronger outcome lower-bound assumption, versus O~(sqrt T) for ClipOGD^0.
- MGATE achieves O~(sqrt(|G|) h(T)^5 sqrt(T)) multigroup Neyman regret for arbitrary finite overlapping group families.
- On Gaussian synthetic data with T=50,000, ClipOGD^SC's regret drops to near 0 for sigma=0.1 while ClipOGD^0's regret keeps increasing with time.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ClipOGD^SC instead of ClipOGD^0 | Non-contextual adaptive ATE design · Synthetic Gaussian data, σ ∈ {0.1, 1, 10} | Neyman regret | Helped |
| Use ClipOGD^SC instead of ClipOGD^0 | Non-contextual adaptive ATE design · Synthetic Gaussian data, σ ∈ {1, 10} | Neyman regret | Mixed |
| Use ClipOGD^SC instead of ClipOGD^0 | Non-contextual adaptive ATE design · Synthetic Gaussian data, σ ∈ {0.1, 1, 10} | Treatment probability convergence | Helped |
| Use ClipOGD^SC instead of ClipOGD^0 | Non-contextual adaptive ATE design · Microfinance | Neyman regret | Helped |
| Use ClipOGD^SC instead of ClipOGD^0 | Non-contextual adaptive ATE design · Microfinance | Treatment probability convergence | Helped |
| Use MGATE instead of ClipOGD^0 or ClipOGD^SC | Contextual adaptive ATE design · Microfinance, overlapping synthetic groups | Group-conditional Neyman regret | Helped |
Surprising findings
- ClipOGD^0's treatment probabilities only converge in the high-noise Gaussian setting (sigma=10), where they happen to match the initial 0.5 probability.
Limitations
- Log T regret requires a stricter outcome lower-bound assumption; the h_inv(1+C/c) term can be large when C/c is large.
- Multigroup regret bound grows with h(T)^5 and sqrt(|G|), and groups in experiments were synthetic post-hoc constructions using unobservable information.
- Wald-type confidence intervals are not proven; only conservative Chebyshev-type intervals are.
Experimental setup
Datasets: synthetic Gaussian outcomes Egypt microfinance dataset
Metrics: Neyman regret treatment probability convergence
Baselines: ClipOGD^0 Bernoulli nonadaptive design
Builds on: ClipOGD SOLO FTRL sleeping experts
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