## Generalized binary search (2008)

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Venue: | In Proceedings of the 46th Allerton Conference on Communications, Control, and Computing |

Citations: | 30 - 0 self |

### BibTeX

@INPROCEEDINGS{Nowak08generalizedbinary,

author = {Robert Nowak},

title = {Generalized binary search},

booktitle = {In Proceedings of the 46th Allerton Conference on Communications, Control, and Computing},

year = {2008},

pages = {568--574}

}

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### Abstract

This paper addresses the problem of noisy Generalized Binary Search (GBS). GBS is a well-known greedy algorithm for determining a binary-valued hypothesis through a sequence of strategically selected queries. At each step, a query is selected that most evenly splits the hypotheses under consideration into two disjoint subsets, a natural generalization of the idea underlying classic binary search. GBS is used in many applications, including fault testing, machine diagnostics, disease diagnosis, job scheduling, image processing, computer vision, and active learning. In most of these cases, the responses to queries can be noisy. Past work has provided a partial characterization of GBS, but existing noise-tolerant versions of GBS are suboptimal in terms of query complexity. This paper presents an optimal algorithm for noisy GBS and demonstrates its application to learning multidimensional threshold functions. 1