# Optimization under Decision-Dependent Uncertainty

arXiv: https://arxiv.org/abs/1611.07992 · HTML: https://mlsanity.com/paper/1611.07992/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2016.

## Built on by (most cited first, 3 of 3)

- [Enhancing Electricity-System Resilience with Adaptive Robust Optimization and Conformal Uncertainty Characterization](https://mlsanity.com/paper/2505.11627/) (2025)
- [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)

## Abstract (arXiv)

The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes a step towards generalizing robust linear optimization to problems with decision-dependent uncertainties. In general settings, we show these problems to be NP-complete. To alleviate the computational inefficiencies, we introduce a class of uncertainty sets whose size depends on binary decisions. We propose reformulations that improve upon alternative standard linearization techniques. To illustrate the advantages of this framework, a shortest path problem is discussed, where the uncertain arc lengths are affected by decisions. Beyond the modeling and performance advantages, the proposed notion of proactive uncertainty control also mitigates over conservatism of current robust optimization approaches.