# Infinite-Horizon Distributionally Robust Regret-Optimal Control

arXiv: https://arxiv.org/abs/2406.07248 · HTML: https://mlsanity.com/paper/2406.07248/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2024.

## Built on by (most cited first, 1 of 1)

- [Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets](https://mlsanity.com/paper/2512.10906/) (2025)

## Abstract (arXiv)

We study the infinite-horizon distributionally robust (DR) control of linear systems with quadratic costs, where disturbances have unknown, possibly time-correlated distribution within a Wasserstein-2 ambiguity set. We aim to minimize the worst-case expected regret-the excess cost of a causal policy compared to a non-causal one with access to future disturbance. Though the optimal policy lacks a finite-order state-space realization (i.e., it is non-rational), it can be characterized by a finite-dimensional parameter. Leveraging this, we develop an efficient frequency-domain algorithm to compute this optimal control policy and present a convex optimization method to construct a near-optimal state-space controller that approximates the optimal non-rational controller in the mathitH_∞-norm. This approach avoids solving a computationally expensive semi-definite program (SDP) that scales with the time horizon in the finite-horizon setting.