Poster
Active Learning of General Halfspaces: Label Queries vs Membership Queries
Ilias Diakonikolas · Daniel Kane · Mingchen Ma
West Ballroom A-D #5608
Abstract:
We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces under the Gaussian distribution on in the presence of some form of query access. In the classical pool-based active learning model, where the algorithm isallowed to make adaptive label queries to previously sampled points, we establish a strong information-theoretic lower bound ruling out non-trivialimprovements over the passive setting. Specifically, we show thatany active learner requires label complexity of , where is the number of unlabeled examples. Specifically, to beat the passive label complexity of , an active learner requires a pool of unlabeled samples.On the positive side, we show that this lower bound can be circumvented with membership query access, even in the agnostic model. Specifically, we give a computationally efficient learner with query complexity of achieving error guarantee of . Here is the bias and is the 0-1 loss of the optimal halfspace. As a corollary, we obtain a strong separation between the active and membership query models. Taken together, our results characterize the complexity of learning general halfspaces under Gaussian marginals in these models.
Chat is not available.