Adaptive Distributionally Robust Optimization
By Dimitris J. Bertsimas, Melvyn Sim, Meilin Zhang. Management Sciences, 2019
310 citations recorded by the source corpus.
We develop a modular and tractable framework for solving an adaptive distributionally robust linear optimization problem, where we minimize the worst-case expected cost over an ambiguity set of probability distributions. The adaptive distributionally robust optimization framework caters for dynamic decision making, where decisions adapt to the uncertain outcomes as they unfold in stages. For tractability considerations, we focus on a class of second-order conic (SOC) representable ambiguity set, though our results can easily be extended to more general conic representations. We show that the adaptive distributionally robust linear optimization problem can be formulated as a classical robust optimization problem. To obtain a tractable formulation, we approximate the adaptive distributionally robust optimization problem using linear decision rule (LDR) techniques. More interestingly, by incorporating the primary and auxiliary random variables of the lifted ambiguity set in the LDR approximation, we can sign...
View Paper: https://www.semanticscholar.org/paper/912ce0d4801c5b314e39ad1ef5117fad7f824411
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Citations in the corpus
- Optimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming (2019, methodology): “12 To account for the sequential decision-making process, researchers recently developed the adaptive DRO method by incorporating recourse decision variables [123, 124].”
- Distributionally Robust Optimization: A Review (2019, methodology): “[44], they show that their approach improves the solutions obtained in Bertsimas et al.”