# Competitive Control

arXiv: https://arxiv.org/abs/2107.13657 · HTML: https://mlsanity.com/paper/2107.13657/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 28 Jul 2021.

## Builds on (most cited first, 12 of 12)

- [Online Control with Adversarial Disturbances](https://mlsanity.com/paper/1902.08721/) (2019)
- [Thinking Fast and Slow: Optimization Decomposition Across Timescales](https://mlsanity.com/paper/1704.07785/) (2017)
- [The Nonstochastic Control Problem](https://mlsanity.com/paper/1911.12178/) (2019)
- [Logarithmic Regret for Adversarial Online Control](https://mlsanity.com/paper/2003.00189/) (2020)
- [Adaptive Regret for Control of Time-Varying Dynamics](https://mlsanity.com/paper/2007.04393/) (2020)
- [Smoothed Online Convex Optimization in High Dimensions via Online Balanced Descent](https://mlsanity.com/paper/1803.10366/) (2018)
- [Non-stationary Online Learning with Memory and Non-stochastic Control](https://mlsanity.com/paper/2102.03758/) (2021)
- [Beyond Online Balanced Descent: An Optimal Algorithm for Smoothed Online Optimization](https://mlsanity.com/paper/1905.12776/) (2019)
- [Smoothed Online Optimization for Regression and Control](https://mlsanity.com/paper/1810.10132/) (2018)
- [The Power of Linear Controllers in LQR Control](https://mlsanity.com/paper/2002.02574/) (2020)
- [Regret-optimal Estimation and Control](https://mlsanity.com/paper/2106.12097/) (2021)
- [Regret-optimal measurement-feedback control](https://mlsanity.com/paper/2011.12785/) (2020)

## Built on by (most cited first, 8 of 8)

- [Beyond Black-Box Advice: Learning-Augmented Algorithms for MDPs with Q-Value Predictions](https://mlsanity.com/paper/2307.10524/) (2023)
- [Best of Both Worlds in Online Control: Competitive Ratio and Policy Regret](https://mlsanity.com/paper/2211.11219/) (2022)
- [Adaptive Online Non-stochastic Control](https://mlsanity.com/paper/2310.02261/) (2023)
- [Optimistic Online Non-stochastic Control via FTRL](https://mlsanity.com/paper/2404.03309/) (2024)
- [Optimal Competitive-Ratio Control](https://mlsanity.com/paper/2206.01782/) (2022)
- [Online estimation and control with optimal pathlength regret](https://mlsanity.com/paper/2110.12544/) (2021)
- [Follow the Clairvoyant: an Imitation Learning Approach to Optimal Control](https://mlsanity.com/paper/2211.07389/) (2022)
- [Consistent Model Chasing Is Minimax Optimal: The Exact Value of Scalar Adversarial Adaptive Control under Large Parametric Uncertainty](https://mlsanity.com/paper/2608.13651/) (2026)

## Abstract (arXiv)

We consider control from the perspective of competitive analysis. Unlike much prior work on learning-based control, which focuses on minimizing regret against the best controller selected in hindsight from some specific class, we focus on designing an online controller which competes against a clairvoyant offline optimal controller. A natural performance metric in this setting is competitive ratio, which is the ratio between the cost incurred by the online controller and the cost incurred by the offline optimal controller. Using operator-theoretic techniques from robust control, we derive a computationally efficient state-space description of the the controller with optimal competitive ratio in both finite-horizon and infinite-horizon settings. We extend competitive control to nonlinear systems using Model Predictive Control (MPC) and present numerical experiments which show that our competitive controller can significantly outperform standard H2 and H∞ controllers in the MPC setting.