论文标题
不确定性集的非参数估计以进行强大优化
Nonparametric Estimation of Uncertainty Sets for Robust Optimization
论文作者
论文摘要
我们研究了一种数据驱动的方法，用于构建可靠优化问题的不确定性集，其中不确定的问题参数被建模为随机变量，其关节概率分布尚不清楚。仅依靠从该分布中得出的独立样本，我们提供了一种非参数方法来估计不确定性集，其概率质量可以保证以高置信度近似给定的目标质量。我们认为的非参数估计量也被证明是遵守无分布的有限样本性能界限，这暗示了它们在概率上与给定目标质量的收敛性。除了有效计算外，提出的估计量还会导致不确定性集，从而为大型约束功能带来了可触及的可靠性优化问题。
We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only on independent samples drawn from this distribution, we provide a nonparametric method to estimate uncertainty sets whose probability mass is guaranteed to approximate a given target mass within a given tolerance with high confidence. The nonparametric estimators that we consider are also shown to obey distribution-free finite-sample performance bounds that imply their convergence in probability to the given target mass. In addition to being efficient to compute, the proposed estimators result in uncertainty sets that yield computationally tractable robust optimization problems for a large family of constraint functions.
