# Distributionally Robust Optimization using Cost-Aware Ambiguity Sets

arXiv: https://arxiv.org/abs/2303.09408 · HTML: https://mlsanity.com/paper/2303.09408/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 43 references that are in the map.
- First posted on arXiv 16 Mar 2023.

## Builds on (most cited first, 10 of 10)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Distributionally Robust Optimization: A Review](https://mlsanity.com/paper/1908.05659/) (2019)
- [From Data to Decisions: Distributionally Robust Optimization is Optimal](https://mlsanity.com/paper/1704.04118/) (2017)
- [Data-driven distributionally robust LQR with multiplicative noise](https://mlsanity.com/paper/1912.09990/) (2019)
- [Distributionally robust risk map for learning-based motion planning and control: A semidefinite programming approach](https://mlsanity.com/paper/2105.00657/) (2021)
- [Risk-averse model predictive control](https://mlsanity.com/paper/1704.00342/) (2017)
- [A General Framework for Learning-Based Distributionally Robust MPC of Markov Jump Systems](https://mlsanity.com/paper/2106.00561/) (2021)
- [Safe, Learning-Based MPC for Highway Driving under Lane-Change Uncertainty: A Distributionally Robust Approach](https://mlsanity.com/paper/2206.13319/) (2022)
- [Risk-averse risk-constrained optimal control](https://mlsanity.com/paper/1903.06749/) (2019)

## Abstract (arXiv)

We present a novel framework for distributionally robust optimization (DRO), called cost-aware DRO (CADRO). The key idea of CADRO is to exploit the cost structure in the design of the ambiguity set to reduce conservatism. Particularly, the set specifically constrains the worst-case distribution along the direction in which the expected cost of an approximate solution increases most rapidly. We prove that CADRO provides both a high-confidence upper bound and a consistent estimator of the out-of-sample expected cost, and show empirically that it produces solutions that are substantially less conservative than existing DRO methods, while providing the same guarantees.