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Decision-dependent Distributionally Robust Optimization
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abstract
This work presents a new Distributionally Robust Optimization approach, using $p$-Wasserstein metrics, to analyze a stochastic program in a general context. The ambiguity set in this approach depends on the decision variable and is represented as a ball where both the center and the radius depend on the decision variable. We show that, under Lipschitz's assumptions for the objective function, our approach can be reformulated as a finite-dimensional optimization problem, which is sometimes convex. In addition, we numerically compare our proposed approach with the standard formulation of distributionally robust optimization, which typically does not use ambiguity sets dependent on the decision variable, in the context of portfolio optimization.
Forward citations
Cited by 2 Pith papers
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Residuals-Based Contextual Distributionally Robust Optimization with Decision-Dependent Uncertainty: Theoretical Guarantees and Decomposition Algorithm
Proposes residuals-based contextual DRO with decision-dependent uncertainty using regression, provides statistical guarantees, and develops a convergent Benders decomposition algorithm.
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Wasserstein Robust Performative Prediction via Lagrangian Relaxation
A Wasserstein robust performative prediction framework with decision-dependent ambiguity claims linear convergence for two retraining algorithms, but the central convergence proof is not supported by the stated assumptions.
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