Bounds for Vector-Valued Function Estimation
  We present a framework to derive risk bounds for vector-valued learning with a broad class of feature maps and loss functions. Multi-task learning and one-vs-all multi-category learning are treated as examples. We discuss in detail vector-valued functions with one hidden layer, and demonstrate that the conditions under which shared representations are beneficial for multi- task learning are equally applicable to multi-category learning. 
Andreas Maurer and Massimiliano Pontil
stat.ML cs.LG