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A Competitive Algorithm for Agnostic Active Learning

Yihan Zhou · Eric Price

Great Hall & Hall B1+B2 (level 1) #1622
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[ Paper [ Poster [ OpenReview
Tue 12 Dec 3:15 p.m. PST — 5:15 p.m. PST

Abstract: For some hypothesis classes and input distributions, \emph{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 \emph{competitive} with the optimal algorithm for any binary hypothesis class $H$ and distribution $\mathcal{D}_X$ 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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