Generalized Risk-Aversion in Stochastic Multi-Armed Bandits
  We consider the problem of minimizing the regret in stochastic multi-armed bandit, when the measure of goodness of an arm is not the mean return, but some general function of the mean and the variance.We characterize the conditions under which learning is possible and present examples for which no natural algorithm can achieve sublinear regret. 
Alexander Zimin and Rasmus Ibsen-Jensen and Krishnendu Chatterjee
cs.LG stat.ML