Semi-parametric inference based on adaptively collected data
This addresses statistical inference challenges in adaptive data collection, such as in bandit algorithms, but appears incremental as it builds on existing semi-parametric methods.
The paper tackles the problem of constructing confidence intervals for semi-parametric models with adaptively collected data, where standard estimators fail to be asymptotically normal, and provides conditions for asymptotic normality with results applied to bandit problems.
Many standard estimators, when applied to adaptively collected data, fail to be asymptotically normal, thereby complicating the construction of confidence intervals. We address this challenge in a semi-parametric context: estimating the parameter vector of a generalized linear regression model contaminated by a non-parametric nuisance component. We construct suitably weighted estimating equations that account for adaptivity in data collection, and provide conditions under which the associated estimates are asymptotically normal. Our results characterize the degree of "explorability" required for asymptotic normality to hold. For the simpler problem of estimating a linear functional, we provide similar guarantees under much weaker assumptions. We illustrate our general theory with concrete consequences for various problems, including standard linear bandits and sparse generalized bandits, and compare with other methods via simulation studies.