Bounded Memory Active Learning through Enriched Queries

Abstract

The explosive growth of easily-accessible unlabeled data has lead to growing interest in active learning, a paradigm in which data-hungry learning algorithms adaptively select informative examples in order to lower prohibitively expensive labeling costs. Unfortunately, in standard worst-case models of learning, the active setting often provides no improvement over non-adaptive algorithms. To combat this, a series of recent works have considered a model in which the learner may ask enriched queries beyond labels. While such models have seen success in drastically lowering label costs, they tend to come at the expense of requiring large amounts of memory. In this work, we study what families of classifiers can be learned in bounded memory. To this end, we introduce a novel streaming-variant of enriched-query active learning along with a natural combinatorial parameter called lossless sample compression that is sufficient for learning not only with bounded memory, but in a query-optimal and computationally efficient manner as well. Finally, we give three fundamental examples of classifier families with small, easy to compute lossless compression schemes when given access to basic enriched queries: axis-aligned rectangles, decision trees, and halfspaces in two dimensions.

Active Learning Polynomial Threshold Functions

“…Active Learning with Enriched Queries: Our work also fits into a long line of recent studies on learning with natural enriched queries. As previously mentioned, Angluin's [19] original membership query model can be viewed in this vein, and many types of specific enriched queries such as comparisons [25,4,5,6,3,8,7,26,27,9,28], cluster-queries [29,30,31,32,33,34,35,36,37], mistake queries [38], separation queries [39], and more have been studied since. Our work relies most closely on the general framework for active learning with enriched queries introduced by KLMZ [3] in 2017, which we discuss in greater depth in Section 2.5.…”

“…This algorithm corresponds to using a 'restricted inference rule' that only infers within such monotone sections. A variant of KLMZ's algorithm for restricted inference is formalized in [28], and has the same guarantees. KLMZ's original algorithm can also be performed in polynomial time, but requires the points to have finite bit complexity which can be avoided with our argument.…”