Statistical Optimization in High Dimensions

摘要: We consider optimization problems whose parameters are known only approximately, based on noisy samples. Of particular interest is the high-dimensional regime, where number of samples roughly equal to dimensionality problem, and noise magnitude may greatly exceed signal itself. This setup falls far outside traditional scope Robust Stochastic optimization. propose three algorithms address this setting, combining ideas from statistics, machine learning, robust In important case artificially increases parameters, we show that reduction can result in high-quality solutions at reduced computational cost.