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We study the performance of a wide class of convex optimization-basedestimators for recovering a signal from corrupted one-bit measurements inhigh-dimensions. Our general result predicts sharply the performance of suchestimators in the linear asymptotic regime when the measurement vectors haveentries IID Gaussian. This includes, as a special case, the previously studiedleast-squares estimator and various novel results for other popular estimatorssuch as least-absolute deviations, hinge-loss and logistic-loss. Importantly,we exploit the fact that our analysis holds for generic convex loss functionsto prove a bound on the best achievable performance across the entire class ofestimators. Numerical simulations corroborate our theoretical findings andsuggest they are accurate even for relatively small problem dimensions.

Sharp Guarantees for Solving Random Equations with One-Bit Information