Minimax analysis of stochastic problems

By Alexander Shapiro, Anton J. Kleywegt. Optim. Methods Softw., 2002

298 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/8f6057c5347f75d47b7afcf0bfea1413138bf69f

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In Control and Systems Engineering

In Management Science and Operations Research

Citations in the corpus

Distributionally robust joint chance constraints with second-order moment information (2011, methodology): “Proof By using (6), the Worst-Case CVaR in (8) can be expressed as sup P∈P P-CVaR ( y0(x)+ y(x)Tξ̃ ) = sup P∈P inf β∈R { β + 1 EP ( (y0(x)+ y(x)Tξ̃ − β)+ )} = inf β∈R { β + 1 sup P∈P EP ( (y0(x)+ y(x)T ξ̃ − β)+ )} , (9) where the interchange of the maximization and minimization operations is justifi”
Robust Dynamic Programming (2005, methodology): “Shapiro and Kleywegt [23] investigate ambiguity in the context of stochastic programming and propose a sampling-based method for solving the maximin problem.”
Distributionally Robust Optimization and Its Tractable Approximations (2010, methodology): “This approach was pioneered by Žáčková (1966) and studied in many other works (e.g., Dupačová 1987, Breton and El Hachem 1995, Shapiro and Kleywegt 2002).”
Decomposition of Uncertainty in Bayesian Deep Learning for Efficient and Risk-sensitive Learning (2017, methodology): “While using uncertainties over transition probabilities to avoid worst-case behavior has been well-studied in discrete MDPs (e.g. (Shapiro & Kleywegt, 2002; Nilim & El Ghaoui, 2005; Bagnell et al., 2001), to our knowledge, our work is the first to consider continuous non-linear functions with…”
Robust Linear Optimization With Recourse (2009, background): “Although Shapiro and Ahmed [31] and Shapiro and Kleywegt [32] have studied specific classes of problems for which the minimax framework leads to traditional stochastic formulations, no such approach has been developed to date for the general case.”
Reinforcement Learning under Model Mismatch (2017, methodology): “A Bayesian approach was proposed by [21] which requires perfect knowledge of the prior distribution on transition matrices.”
Robust Control of Markov Decision Processes with Uncertain Transition Matrices (2005, methodology): “A Bayesian approach such as described by Shapiro and Kleywegt (2002) requires a perfect knowledge of the whole prior distribution on the transition matrix, making it difficult to apply in practice.”
Robustness in Markov Decision Problems with Uncertain Transition Matrices (2003, methodology): “A Bayesian approach such as described by [9] requires a perfect knowledge of the whole prior distribution on the transition matrix, making it difficult to apply in practice.”
Monte Carlo sampling-based methods for stochastic optimization (2014, methodology): “Shapiro and Kleywegt [224] study the application of Monte Carlo sampling—more specifically, the SAA approach—for this type of problem.”
Ambiguous chance constrained problems and robust optimization (2006, background): “The minimax formulation has a long history in stochastic programing [46, 8, 16, 17, 30, 42 , 40, 41].”
Adaptive Distributionally Robust Optimization (2019, methodology): “…such models have been extended to minimax stochastic optimization models (see, for instance, ˇ Z´aˇckov´a 1966, Dupacova 1987, Breton and EI Hachem 1995, Shapiro and Kleywegt 2002, Shapiro and Ahmed 2004), and recently to distributionally robust optimization models (see, for instance, Chen et al.…”
Distributionally Robust Convex Optimization (2014, background): “, Lagoa and Barmish [43], Shapiro and Ahmed [57] and Shapiro and Kleywegt [58].”
Distributionally Robust Stochastic Optimization with Wasserstein Distance (2016, background): “One chooses a set M of probability distributions to hedge against, and then ﬁnds a decision that provides the best hedge against the set M of distributions by solving the following minmax problem: (DRSO) Such a minmax approach has its roots in Von Neumann’s game theory and has been used in many ﬁeld”
Distributionally Robust Optimization: A Review (2019, background): “Motivated by the drawback of moment-based DRO problems, Gao and Kleywegt [111] study DRO formed via various ambiguity sets of probability distributions that incorporate the dependence structure between the uncertain parameters.”