# Regret-optimal measurement-feedback control

arXiv: https://arxiv.org/abs/2011.12785 · HTML: https://mlsanity.com/paper/2011.12785/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2020.

## Built on by (most cited first, 5 of 5)

- [Regret-optimal Estimation and Control](https://mlsanity.com/paper/2106.12097/) (2021)
- [Competitive Control](https://mlsanity.com/paper/2107.13657/) (2021)
- [Offline Reinforcement Learning via Inverse Optimization](https://mlsanity.com/paper/2502.20030/) (2025)
- [Constrained Online Decision-Making: A Unified Framework](https://mlsanity.com/paper/2505.07101/) (2025)
- [Online estimation and control with optimal pathlength regret](https://mlsanity.com/paper/2110.12544/) (2021)

## Abstract (arXiv)

We consider measurement-feedback control in linear dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing an online controller which competes with the optimal dynamic sequence of control actions selected in hindsight, instead of the best controller in some specific class of controllers. This formulation of regret is attractive when the environment changes over time and no single controller achieves good performance over the entire time horizon. We show that in the measurement-feedback setting, unlike in the full-information setting, there is no single offline controller which outperforms every other offline controller on every disturbance, and propose a new H2-optimal offline controller as a benchmark for the online controller to compete against. We show that the corresponding regret-optimal online controller can be found via a novel reduction to the classical Nehari problem from robust control and present a tight data-dependent bound on its regret.