An efficient black-box reduction from PQ to TDS learning for any Boolean concept class in the distribution-free setting implies hardness for TDS learning of halfspaces, while membership queries enable efficient PQ learning of halfspaces via iterative Forster transforms.
Advances in neural information processing systems , volume=
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Equivalence of Coarse and Fine-Grained Models for Learning with Distribution Shift
An efficient black-box reduction from PQ to TDS learning for any Boolean concept class in the distribution-free setting implies hardness for TDS learning of halfspaces, while membership queries enable efficient PQ learning of halfspaces via iterative Forster transforms.