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We consider the problem of robust polynomial regression, where one receivessamples $(x_i, y_i)$ that are usually within $\sigma$ of a polynomial $y =p(x)$, but have a $\rho$ chance of being arbitrary adversarial outliers.Previously, it was known how to efficiently estimate $p$ only when $\rho <\frac{1}{\log d}$. We give an algorithm that works for the entire feasiblerange of $\rho < 1/2$, while simultaneously improving other parameters of theproblem. We complement our algorithm, which gives a factor 2 approximation,with impossibility results that show, for example, that a $1.09$ approximationis impossible even with infinitely many samples.

Robust polynomial regression up to the information theoretic limit