Simulation-Based Inference for Adaptive Experiments
This addresses the need for more powerful and flexible inference methods in adaptive experiments, which are increasingly used to improve outcomes and efficiency in fields like clinical trials, but the approach is incremental as it builds on existing simulation techniques.
The paper tackles the problem of conducting inference after adaptive sampling in multi-arm bandit experiments, where current methods are either restricted or underpowered, and proposes a simulation-based approach that achieves desired coverage while reducing confidence interval widths by up to 50%.
Multi-arm bandit experimental designs are increasingly being adopted over standard randomized trials due to their potential to improve outcomes for study participants, enable faster identification of the best-performing options, and/or enhance the precision of estimating key parameters. Current approaches for inference after adaptive sampling either rely on asymptotic normality under restricted experiment designs or underpowered martingale concentration inequalities that lead to weak power in practice. To bypass these limitations, we propose a simulation-based approach for conducting hypothesis tests and constructing confidence intervals for arm specific means and their differences. Our simulation-based approach uses positively biased nuisances to generate additional trajectories of the experiment, which we call \textit{simulation with optimism}. Using these simulations, we characterize the distribution potentially non-normal sample mean test statistic to conduct inference. We provide guarantees for (i) asymptotic type I error control, (ii) convergence of our confidence intervals, and (iii) asymptotic strong consistency of our estimator over a wide variety of common bandit designs. Our empirical results show that our approach achieves the desired coverage while reducing confidence interval widths by up to 50%, with drastic improvements for arms not targeted by the design.