  The group testing problem consists of determining a small set of defective
items from a larger set of items based on a number of possibly-noisy tests, and
is relevant in applications such as medical testing, communication protocols,
pattern matching, and many more. One of the defining features of the group
testing problem is the distinction between the non-adaptive and adaptive
settings: In the non-adaptive case, all tests must be designed in advance,
whereas in the adaptive case, each test can be designed based on the previous
outcomes. While tight information-theoretic limits and near-optimal practical
algorithms are known for the adaptive setting in the absence of noise,
surprisingly little is known in the noisy adaptive setting. In this paper, we
address this gap by providing information-theoretic achievability and converse
bounds under various noise models, as well as a slightly weaker achievability
bound for a computationally efficient variant. These bounds are shown to be
tight or near-tight in a broad range of scaling regimes, particularly at low
noise levels. The algorithms used for the achievability results have the
notable feature of only using two or three stages of adaptivity.
