Likelihood robust optimization for data-driven problems
Likelihood robust optimization for data-driven problems
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DOI：
10.1007/s10287-015-0240-3
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发表时间：
2013-07
影响因子：
0.9
通讯作者：
Zizhuo Wang;P. Glynn;Y. Ye
中科院分区：
文献类型：
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作者：
Zizhuo Wang;P. Glynn;Y. Ye
我们考虑在不确定环境中的最优决策问题。特别是，我们考虑的情况下，输入的分布是未知的，但有一些历史数据从分布。在本文中，我们提出了一种新的类型的分布鲁棒优化模型称为类鲁棒优化（LRO）模型，这类问题。与以前专注于某些参数（例如，均值、方差等）的输入分布，我们利用历史数据，并定义可访问的分布集，只包含那些分布，使观察到的数据达到一定程度的可能性。然后，我们制定的目标问题作为一个优化的期望值的目标函数在最坏情况下的分布在该集合。我们的模型通过排除不切实际的分布，同时保持任何统计上可能的结果的解决方案的鲁棒性，避免了一些先前的鲁棒方法的过度保守性。我们目前的统计分析，我们的模型使用贝叶斯统计和经验似然理论。具体来说，我们证明了我们的分布集的渐近行为，并建立我们的模型和其他分布鲁棒模型之间的关系。为了测试我们的模型的性能，我们将其应用到报童问题和投资组合选择问题。测试结果表明，我们的模型的解决方案确实有令人满意的性能。
We consider optimal decision-making problems in an uncertain environment. In particular, we consider the case in which the distribution of the input is unknown, yet there is some historical data drawn from the distribution. In this paper, we propose a new type of distributionally robust optimization model called thelikelihood robust optimization(LRO) model for this class of problems. In contrast to previous work on distributionally robust optimization that focuses on certain parameters (e.g., mean, variance, etc.) of the input distribution, we exploit the historical data and define the accessible distribution set to contain only those distributions that make the observed data achieve a certain level of likelihood. Then we formulate the targeting problem as one of optimizing the expected value of the objective function under the worst-case distribution in that set. Our model avoids the over-conservativeness of some prior robust approaches by ruling out unrealistic distributions while maintaining robustness of the solution for any statistically likely outcomes. We present statistical analyses of our model using Bayesian statistics and empirical likelihood theory. Specifically, we prove the asymptotic behavior of our distribution set and establish the relationship between our model and other distributionally robust models. To test the performance of our model, we apply it to the newsvendor problem and the portfolio selection problem. The test results show that the solutions of our model indeed have desirable performance.