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Simulation-Based Inference for Adaptive Experiments
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Proposes simulation with optimism: resimulates bandit experiments under the null with positively biased arm-mean nuisances to build a test and confidence intervals for arm means and differences, with asymptotic type I error control under common adaptive designs.
Problem
After-study inference (hypothesis tests and confidence intervals for arm means and differences) on data from adaptive bandit experiments, where standard Wald intervals fail and anytime-valid methods are underpowered.
Approach
Simulate experiment trajectories under the null with optimistic (positively biased, vanishing-bias) estimates of nuisance arm means and variances, and compare the observed sample mean to the simulated distribution; this avoids asymptotic normality and grid scanning over nuisances while keeping type I error control for designs like ETC, UCB, and clipped reward-maximizing schemes.
Key results
- Simulation-based CIs reduce average width by up to 50% relative to the next best method, most strongly for the worst (undersampled) arm, while keeping coverage comparable to asymptotic baselines (alpha=0.1).
- With plug-in nuisance estimates, realized type I error in a two-arm ETC design was up to 12% above the nominal level; optimistic nuisances match the nominal level.
- On the real-world MTurk data, intervals for the three lowest-support proposals shrink by up to roughly 50% versus the reported intervals; best arms widen by at most 0.059.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use simulation-based inference with optimistic nuisance estimates instead of the next-best method | Adaptive experiments · Synthetic worst-arm setting | confidence interval width: up to 50% | Helped |
| Use simulation-based inference instead of the reported intervals | Adaptive MTurk experiment · Three lowest-support proposals | confidence interval width: up to roughly 50% | Helped |
| Use simulation-based inference instead of the best-performing baseline | Adaptive MTurk experiment · Best-performing arms | confidence interval width: 0.059 | Hurt |
| Use simulation-based inference instead of the best-performing baseline | Adaptive MTurk experiment · Worst-performing arms | confidence interval width: up to 0.1 | Helped |
| Use plug-in nuisance estimates rather than optimistic nuisance estimates | Simulation-based inference · Two-arm ETC | type I error: up to 12% larger than desired | Hurt |
| Use vanishing Bias 1 instead of Bias 2 or Bias 3 (ablation) | Simulation-based inference · ETC, null θ₀ = 0.02 and ground truth θ* = 0 | power | Helped |
Surprising findings
- Plug-in nuisance estimates fail to control type I error even at parametric rates in a simple two-arm ETC design, because the simulated and observed test statistic distributions do not match.
Limitations
- Guarantees are asymptotic; finite-sample control is not provided.
- Confidence intervals require a grid of null values that must contain the true parameter, and runtime grows with grid size and simulation count.
- Point estimate heuristic lacks theoretical guarantees.
Experimental setup
Datasets: Synthetic Bernoulli bandit data Real-world MTurk ballot measure adaptive experiment (1000 participants, batched Thompson sampling)
Benchmarks: Synthetic Bernoulli 3-arm setups (worst arm, no signal, best arm) Real-world MTurk ballot measure experiment
Metrics: coverage / type I error average CI width mean squared error type I error rate deviation
Baselines: empirical Bernstein anytime-valid CI variance stabilizing weights (asymptotic) variance minimizing weights (asymptotic) batched Thompson sampling reported intervals
Builds on: Thompson sampling batched design law of iterated logarithm martingale central limit theorem variance stabilizing weights empirical Bernstein anytime-valid inference
Closest papers by meaning
- Inference for Batched Bandits (NeurIPS 2020 · similarity 0.89)
- Are sample means in multi-armed bandits positively or negatively biased? (NeurIPS 2019 · similarity 0.89)
- Optimistic Algorithms for Adaptive Estimation of the Average Treatment Effect (ICML 2025 · similarity 0.88)
- Efficient Adaptive Experimentation with Noncompliance (NeurIPS 2025 · similarity 0.86)
- Noise-Adaptive Confidence Sets for Linear Bandits and Application to Bayesian Optimization (ICML 2024 · similarity 0.86)
- Stronger Neyman Regret Guarantees for Adaptive Experimental Design (ICML 2025 · similarity 0.85)
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