Optimization of the quantile criterion for the convex loss function by a stochastic quasigradient algorithm - Kibzun, Andrey; Matveev, Evgeniy (Annals of operations research, 2012)
A stochastic quasigradient algorithm is suggested for solving the quantile optimization problem with a convex loss function. The algorithm is based on stochastic finite-difference approximations of gradients of the quantile function by using the order statistics. The algorithm convergence almost surely is proved.