Risk minimization by median-of-means tournaments
  We consider the classical statistical learning/regression problem, when the value of a real random variable Y is to be predicted based on the observation of another random variable X. Given a class of functions F and a sample of independent copies of (X, Y ), one needs to choose a function f from F such that f(X) approximates Y as well as possible, in the mean-squared sense. We introduce a new procedure, the so-called median-of-means tournament, that achieves the optimal tradeoff between accuracy and confidence under minimal assumptions, and in particular outperforms classical methods based on empirical risk minimization. 
Gabor Lugosi and Shahar Mendelson
math.ST stat.TH