Characterizing the robustness of Bayesian adaptive experimental designs to active learning bias

Bayesian adaptive experimental design is a form of active learning, which chooses samples to maximize the information they give about uncertain parameters. Prior work has shown that other forms of active learning can suffer from active learning bias, where unrepresentative sampling leads to inconsistent parameter estimates. We show that active learning bias can also afflict Bayesian adaptive experimental design, depending on model misspecification. We analyze the case of estimating a linear model, and show that worse misspecification implies more severe active learning bias. At the same time, model classes incorporating more "noise" - i.e., specifying higher inherent variance in observations - suffer less from active learning bias. Finally, we demonstrate empirically that insights from the linear model can predict the presence and degree of active learning bias in nonlinear contexts, namely in a (simulated) preference learning experiment.