Learning Unions of Rectangles with Queries

We investigate the e cient learnability of unions of k rectangles in the discrete plane f1; : : : ; ng2 with equivalence and membership queries. We exhibit a learning algorithm that learns any union of k rectangles with O(k3 log n) queries, while the time complexity of this algorithm is bounded by O(k5 logn). We design our learning algorithm by nding \corners" and \edges" for rectangles contained in the target concept and then constructing the target concept from those \corners" and \edges". Our result provides a rst approach to on-line learning of nontrivial subclasses of unions of intersections of halfspaces with equivalence and membership queries.

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