# Distributionally Robust Optimization with Decision Dependent Ambiguity Sets

arXiv: https://arxiv.org/abs/1806.09215 · HTML: https://mlsanity.com/paper/1806.09215/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2018.

## Built on by (most cited first, 6 of 6)

- [Decision-Dependent Stochastic Optimization: The Role of Distribution Dynamics](https://mlsanity.com/paper/2503.07324/) (2025)
- [Distributionally Robust Graph Learning from Smooth Signals under Moment Uncertainty](https://mlsanity.com/paper/2105.05458/) (2021)
- [Decision-Dependent Distributionally Robust Markov Decision Process Method in Dynamic Epidemic Control](https://mlsanity.com/paper/2306.14051/) (2023)
- [Robust Risk-Sensitive Reinforcement Learning with Conditional Value-at-Risk](https://mlsanity.com/paper/2405.01718/) (2024)
- [On Tractability, Complexity, and Mixed-Integer Convex Programming Representability of Distributionally Favorable Optimization](https://mlsanity.com/paper/2401.17899/) (2024)
- [Global Optimisation of Black-Box Functions with Generative Models in the Wasserstein Space](https://mlsanity.com/paper/2407.11917/) (2024)

## Abstract (arXiv)

We study decision dependent distributionally robust optimization models, where the ambiguity sets of probability distributions can depend on the decision variables. These models arise in situations with endogenous uncertainty. The developed framework includes two-stage decision dependent distributionally robust stochastic programming as a special case. Decision dependent generalizations of five types of ambiguity sets are considered. These sets are based on bounds on moments, Wasserstein metric, φ-divergence and Kolmogorov-Smirnov test. For the finite support case, we use linear, conic or Lagrangian duality to give reformulations of the models with a finite number of constraints. These reformulations allow solutions of such problems using global optimization techniques. Certain reformulations give rise to non-convex semi-infinite programs. Techniques from global optimization and semi-infinite programming can be used to solve these reformulations.