A Bayesian Risk Approach to Data-driven Stochastic Optimization: Formulations and Asymptotics
A Bayesian Risk Approach to Data-driven Stochastic Optimization: Formulations and Asymptotics
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DOI：
10.1137/16m1101933
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发表时间：
2016-09
期刊：
影响因子：
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通讯作者：
Di Wu;Helin Zhu;Enlu Zhou
中科院分区：
文献类型：
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作者：
Di Wu;Helin Zhu;Enlu Zhou
一大类随机程序涉及优化相对于实际未知的潜在分布所采取的期望。一种解决分布不确定性的流行方法，称为分布稳健优化，是通过一组不确定的候选分布来对冲最坏的情况。然而，人们已经观察到，不确定集的不适当构造有时会导致过于保守的解。为了探索乐观地忽略分布不确定性和悲观地关注最坏情况之间的中间地带，我们提出了参数基础分布的贝叶斯风险优化框架，即优化应用于未知分布参数的后验分布的风险泛函。我们特别感兴趣的是四个风险泛函：均值、均值-方差、风险值和条件风险值。为了解开兄弟的含义，我们建立了.
A large class of stochastic programs involve optimizing an expectation taken with respect to an underlying distribution that is unknown in practice. One popular approach to addressing the distributional uncertainty, known as the distributionally robust optimization, is to hedge against the worst case over an uncertainty set of candidate distributions. However, it has been observed that inappropriate construction of the uncertainty set can sometimes result in overconservative solutions. To explore the middle ground between optimistically ignoring the distributional uncertainty and pessimistically fixating on the worst-case scenario, we propose a Bayesian risk optimization (BRO) framework for parametric underlying distributions, which is to optimize a risk functional applied to the posterior distribution of an unknown distribution parameter. Of our particular interest are four risk functionals: mean, mean-variance, value-at-risk, and conditional value-at-risk. To unravel the implication of BRO, we establish...