Abstract
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.
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The work was supported by Russian Foundation of Basic Research (project N0 09-08-00369).
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Kibzun, A., Matveev, E. Optimization of the quantile criterion for the convex loss function by a stochastic quasigradient algorithm. Ann Oper Res 200, 183–198 (2012). https://doi.org/10.1007/s10479-011-0987-z
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DOI: https://doi.org/10.1007/s10479-011-0987-z