We study the task of agnostically learning halfspaces under the Gaussian distribution.Specifically, given labeled examples ( mathbfx,y) from an unknown distribution on mathbbR^n times ± 1, whose marginal distribution on mathbfx is the standard Gaussian and the labels y can be arbitrary, the goal is to output a hypothesis with 0-1 loss mathrmOPT+ epsilon, where mathrmOPT is the 0-1 loss of the best-fitting halfspace.We prove a near-optimal computational hardness result for this task, under the wi…