Randomized Quasi-Monte Carlo Methods for Risk-Averse Stochastic Optimization
研究了基于样本的风险规避复合风险泛函的逼近，证明随机拟蒙特卡罗方法比蒙特卡罗方法偏差和均方根误差更小，适用于风险规避随机规划和变分不等式问题。
Abstract We establish epigraphical and uniform laws of large numbers for sample-based approximations of law invariant composite risk functionals. These sample-based approximation schemes include Monte Carlo and certain randomized quasi-Monte Carlo integration methods, such as scrambled net integration. Our results can be applied to the approximation of risk-averse stochastic programs and risk-averse stochastic variational inequalities. Our numerical simulations empirically demonstrate that randomized quasi-Monte Carlo approaches based on scrambled Sobol’ sequences can yield smaller bias and root mean square error than Monte Carlo methods for risk-averse optimization.