A space-bounded learning algorithm for axis-parallel rectangles

Abstract

We consider the on-line learnability from equivalence queries only of axis-parallel rectangles over the discrete grid {1,..., n}^d (BOX ^d _n ). Further we impose the restriction of “k-space-bounded learning”, i.e. the information the learner can store about the history of the learning protocol is restricted to the previous hypothesis and at most k of the examples seen. Our result improves the best known algorithm about learning BOX ^d _n due to Chen and Maass [9]. Their algorithm has learning complexity O(d ² log n) requires space Θ(d ²logn) and time Ω(log(d ²log n)) for each learning step. We present an on-line learning algorithm for BOX ^d _n with the same learning complexity, time complexity O(d ³log n) which is 2d-space-bounded.

Supported in part by the ESPRIT Basic Research Action No 7141 (ALCOM II) and by the DFG grant Di 412/2-1.