  In many settings, such as scientific inference, optimization, and transfer
learning, the learner has a well-defined objective, which can be treated as
estimation of a target parameter, and no intrinsic interest in characterizing
the entire data-generating process. Usually, the learner must also contend with
additional sources of uncertainty or variables -- with nuisance parameters.
Bayesian active learning, or sequential optimal experimental design, can
straightforwardly accommodate the presence of nuisance parameters, and so is a
natural active learning framework for such problems. However, the introduction
of nuisance parameters can lead to bias in the Bayesian learner's estimate of
the target parameters, a phenomenon we refer to as negative interference. We
characterize the threat of negative interference and how it fundamentally
changes the nature of the Bayesian active learner's task. We show that the
extent of negative interference can be extremely large, and that accurate
estimation of the nuisance parameters is critical to reducing it. The Bayesian
active learner is confronted with a dilemma: whether to spend a finite
acquisition budget in pursuit of estimation of the target or of the nuisance
parameters. Our setting encompasses Bayesian transfer learning as a special
case, and our results shed light on the phenomenon of negative transfer between
learning environments.
