Why squared error? (2014)
There is a Kaggle competition right now that uses mean absolute error, and this makes the problem substantially harder. For a practical discussion of techniques used to solve machine learning problems that use mae see the forums in: <a href="https://www.kaggle.com/c/allstate-claims-severity/forums" rel="nofollow">https://www.kaggle.com/c/allstate-claims-severity/forums</a><p>As touched upon in the article, the objective not being differentiable is a big deal for modern machine learning methods.