Simple and practical algorithms for 𝓁p-norm low-rank approximation.

We propose practical algorithms for entrywise l(p)-norm low-rank approximation, for p = 1 or p = infinity. The proposed framework, which is non-convex and gradient-based, is easy to implement and typically attains better approximations, faster, than state of the art.From a theoretical standpoint, we show that the proposed scheme can attain (1 + epsilon)OPT approximations. Our algorithms are not hyperparameter-free: they achieve the desiderata only assuming algorithm's hyperparameters are known apriori-or are at least approximable. I.e., our theory indicates what problem quantities need to be known, in order to get a good solution within polynomial time, and does not contradict to recent inapproximabilty results, as in [46].