arXiv:2310.18786 · v4

A Competitive Algorithm for Agnostic Active Learning

首次提交 2023-10-29 03:01

版本更新 2026-10-28 07:30

雷达观测 2026-10-30 10:23

摘要

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 $O(η)$ error, then our algorithm uses $O(m^* \log |H|)$ queries to get $O(η)$ error. Our algorithm lies in the vein of the splitting-based approach of Dasgupta [2004], which gets a similar result for the realizable ($η= 0$) setting. We also show that it is NP-hard to do better than our algorithm's $O(\log |H|)$ overhead in general.