A Competitive Algorithm for Agnostic Active Learning

• URL: http://arxiv.org/abs/2310.18786v3
• Date: Wed, 22 May 2024 18:58:01 GMT
• Title: A Competitive Algorithm for Agnostic Active Learning
• Authors: Eric Price, Yihan Zhou,
• Abstract summary: Most popular algorithms for active learning express their performance in terms of a parameter called the disagreement coefficient. We get an algorithm that is competitive with the optimal algorithm for any binary hypothesis class $H$ and distribution $D_X$ over $X$. It is NP-hard to do better than our algorithm's $O(log |H|)$ overhead in general.
• Score: 5.4579367210379335
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: For some hypothesis classes and input distributions, active agnostic learning needs exponentially fewer samples than passive learning; for other classes and distributions, it offers little to no improvement. The most popular algorithms for agnostic active learning express their performance in terms of a parameter called the disagreement coefficient, but it is known that these algorithms are inefficient on some inputs. We take a different approach to agnostic active learning, getting an algorithm that is competitive with the optimal algorithm for any binary hypothesis class $H$ and distribution $D_X$ over $X$. In particular, if any algorithm can use $m^*$ queries to get $O(\eta)$ error, then our algorithm uses $O(m^* \log |H|)$ queries to get $O(\eta)$ error. Our algorithm lies in the vein of the splitting-based approach of Dasgupta [2004], which gets a similar result for the realizable ($\eta = 0$) setting. We also show that it is NP-hard to do better than our algorithm's $O(\log |H|)$ overhead in general.

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