期刊
OPERATIONS RESEARCH
卷 70, 期 1, 页码 454-471出版社
INFORMS
DOI: 10.1287/opre.2020.2069
关键词
data-driven optimization; prescriptive analytics; reproducing kernel Hilbert space; regression; optimality
Two methods based on regression in reproducing kernel Hilbert spaces are proposed for solving optimization problems with uncertain parameters. The second method shows improvement in overcoming dimensionality and reducing sample complexity compared to existing methods.
We present two methods, based on regression in reproducing kernel Hilbert spaces, for solving an optimization problem with uncertain parameters for which we have historical data, including auxiliary data. The first method approximates the objective function and the second approximates the optimizer. We provide finite sample guarantees and prove asymptotic optimality for both methods. Computational experiments suggest that at least the second method overcomes a curse of dimensionality that afflicts existing methods, extrapolates better to unseen data, and achieves a many-fold decrease in sample complexity even for small dimensions.
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