Constant-factor approximate proper learning of large-margin halfspaces is essentially settled: an optimal-sample 2^{Õ(1/γ²)}-time learner, plus an ETH-based 2^{(1/γ)^{2-o(1)}} runtime barrier for any proper learner.
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Nearly Tight Bounds for Robust Proper Learning of Halfspaces with a Margin
Constant-factor approximate proper learning of large-margin halfspaces is essentially settled: an optimal-sample 2^{Õ(1/γ²)}-time learner, plus an ETH-based 2^{(1/γ)^{2-o(1)}} runtime barrier for any proper learner.