# Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets

arXiv: https://arxiv.org/abs/2512.10906 · HTML: https://mlsanity.com/paper/2512.10906/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 40 references that are in the map.
- First posted on arXiv 11 Dec 2025.

## Builds on (most cited first, 18 of 18)

- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Wasserstein Distributionally Robust Stochastic Control: A Data-Driven Approach](https://mlsanity.com/paper/1812.09808/) (2018)
- [Regret-optimal Estimation and Control](https://mlsanity.com/paper/2106.12097/) (2021)
- [Distributionally Robust Linear Quadratic Control](https://mlsanity.com/paper/2305.17037/) (2023)
- [Data-driven distributionally robust LQR with multiplicative noise](https://mlsanity.com/paper/1912.09990/) (2019)
- [Distributional robustness in minimax linear quadratic control with Wasserstein distance](https://mlsanity.com/paper/2102.12715/) (2021)
- [Safe Control with Minimal Regret](https://mlsanity.com/paper/2203.00358/) (2022)
- [Wasserstein Distributionally Robust Control of Partially Observable Linear Stochastic Systems](https://mlsanity.com/paper/2212.04644/) (2022)
- [A Distributionally Robust Approach to Regret Optimal Control using the Wasserstein Distance](https://mlsanity.com/paper/2304.06783/) (2023)
- [A unified analysis of convex and non-convex lp-ball projection problems](https://mlsanity.com/paper/2203.00564/) (2022)
- [Recursively feasible Data-driven Distributionally Robust Model Predictive Control with additive disturbances](https://mlsanity.com/paper/2205.04146/) (2022)
- [Wasserstein Distributionally Robust Regret-Optimal Control under Partial Observability](https://mlsanity.com/paper/2307.04966/) (2023)
- [Robust Regret Optimal Control](https://mlsanity.com/paper/2307.14297/) (2023)
- [Distributionally Robust Model Predictive Control: Closed-loop Guarantees and Scalable Algorithms](https://mlsanity.com/paper/2309.12758/) (2023)
- [Distributionally Robust Infinite-horizon Control: from a pool of samples to the design of dependable controllers](https://mlsanity.com/paper/2312.07324/) (2023)
- [A Convex Information Relaxation for Constrained Decentralized Control Design Problems](https://mlsanity.com/paper/1708.03991/) (2017)
- [Performance-Robustness Tradeoffs in Adversarially Robust Control and Estimation](https://mlsanity.com/paper/2305.16415/) (2023)
- [Infinite-Horizon Distributionally Robust Regret-Optimal Control](https://mlsanity.com/paper/2406.07248/) (2024)

## Abstract (arXiv)

We consider a class of finite-horizon, linear-quadratic stochastic control problems, where the probability distribution governing the noise process is unknown but assumed to belong to an ambiguity set consisting of all distributions whose mean and covariance lie within norm balls centered at given nominal values. To cope with this ambiguity, we design causal affine control policies to minimize the worst-case expected regret over all distributions in the ambiguity set. The resulting minimax optimal control problem is shown to admit an equivalent reformulation as a tractable convex program, which can be interpreted as a regularized version of the nominal linear-quadratic stochastic control problem. Based on the dual of this convex reformulation, we develop a scalable projected subgradient method for computing optimal controllers to arbitrary accuracy. Numerical experiments are provided to compare the proposed method with state-of-the-art data-driven control design methods.