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作者：Zhen, Jianzhe; Kuhn, Daniel; Wiesemann, Wolfram
作者单位：Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Imperial College London
摘要：Robust optimization and distributionally robust optimization are modeling paradigms for decision making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from within an ambiguity set, respectively, and a decision is sought that minimizes a cost function under the most adverse outcome of the uncertainty. In this paper, we develop a rigorous and general theory of robust and distributionally robust nonli...
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作者：Xu, Guanglin; Hanasusanto, Grani A.
作者单位：University of North Carolina; University of North Carolina Charlotte; University of Minnesota System; University of Minnesota Twin Cities; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We study decision rule approximations for generic multistage robust linear optimization problems. We examine linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are uncertain, and we explore quadratic decision rules for the case when only the right-hand sides are uncertain. The resulting optimization problems are NP hard but amenable to copositive programming reformulations that give rise to tight, tractable semidefinite programmi...
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作者：Wang, Yining
作者单位：University of Texas System; University of Texas Dallas
摘要：In this paper, we study the nonstationary stochastic optimization problem with bandit feedback and dynamic regret measures. The seminal work of Besbes et al. (2015) shows that, when aggregated function changes are known a priori, a simple restarting algorithm attains the optimal dynamic regret. In this work, we design a stochastic optimi-zation algorithm with fixed step sizes, which, combined with the multiscale sampling framework in existing research, achieves the optimal dynamic regret in no...
