# Logarithmic Regret for Adversarial Online Control

arXiv: https://arxiv.org/abs/2003.00189 · HTML: https://mlsanity.com/paper/2003.00189/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Feb 2020.

## Built on by (most cited first, 30 of 41)

- [Non-stationary Online Learning with Memory and Non-stochastic Control](https://mlsanity.com/paper/2102.03758/) (2021)
- [Efficient Methods for Non-stationary Online Learning](https://mlsanity.com/paper/2309.08911/) (2023)
- [Adversarial Tracking Control via Strongly Adaptive Online Learning with Memory](https://mlsanity.com/paper/2102.01623/) (2021)
- [Lazy OCO: Online Convex Optimization on a Switching Budget](https://mlsanity.com/paper/2102.03803/) (2021)
- [Regret-optimal Estimation and Control](https://mlsanity.com/paper/2106.12097/) (2021)
- [Exploiting the Curvature of Feasible Sets for Faster Projection-Free Online Learning](https://mlsanity.com/paper/2205.11470/) (2022)
- [Competitive Control](https://mlsanity.com/paper/2107.13657/) (2021)
- [Optimal Rates for Bandit Nonstochastic Control](https://mlsanity.com/paper/2305.15352/) (2023)
- [Optimal Dynamic Regret in LQR Control](https://mlsanity.com/paper/2206.09257/) (2022)
- [Model Predictive Control via On-Policy Imitation Learning](https://mlsanity.com/paper/2210.09206/) (2022)
- [Online Convex Optimization with Unbounded Memory](https://mlsanity.com/paper/2210.09903/) (2022)
- [Best of Both Worlds in Online Control: Competitive Ratio and Policy Regret](https://mlsanity.com/paper/2211.11219/) (2022)
- [Online Nonstochastic Control with Adversarial and Static Constraints](https://mlsanity.com/paper/2302.02426/) (2023)
- [Predictive Linear Online Tracking for Unknown Targets](https://mlsanity.com/paper/2402.10036/) (2024)
- [Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamics](https://mlsanity.com/paper/2203.01170/) (2022)
- [PAC-Bayesian bounds for learning LTI-ss systems with input from empirical loss](https://mlsanity.com/paper/2303.16816/) (2023)
- [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)
- [Offline Reinforcement Learning via Inverse Optimization](https://mlsanity.com/paper/2502.20030/) (2025)
- [A Simple, Optimal and Efficient Algorithm for Online Exp-Concave Optimization](https://mlsanity.com/paper/2512.23190/) (2025)
- [Optimal Competitive-Ratio Control](https://mlsanity.com/paper/2206.01782/) (2022)
- [Length independent generalization bounds for deep SSM architectures via Rademacher contraction and stability constraints](https://mlsanity.com/paper/2405.20278/) (2024)
- [Incremental Online Learning of Randomized Neural Network with Forward Regularization](https://mlsanity.com/paper/2412.13096/) (2024)
- [A New Approach to Controlling Linear Dynamical Systems](https://mlsanity.com/paper/2504.03952/) (2025)
- [Parameter-free Dynamic Regret: Time-varying Movement Costs, Delayed Feedback, and Memory](https://mlsanity.com/paper/2602.06902/) (2026)
- [PAC-Bayesian-Like Error Bound for a Class of Linear Time-Invariant Stochastic State-Space Models](https://mlsanity.com/paper/2212.14838/) (2022)
- [Online Residual Learning from Offline Experts for Pedestrian Tracking](https://mlsanity.com/paper/2409.04069/) (2024)
- [Regret-Optimal LQR Control](https://mlsanity.com/paper/2105.01244/) (2021)
- [Rate-matching the regret lower-bound in the linear quadratic regulator with unknown dynamics](https://mlsanity.com/paper/2202.05799/) (2022)
- [Learning to Control under Time-Varying Environment](https://mlsanity.com/paper/2206.02507/) (2022)

## Abstract (arXiv)

We introduce a new algorithm for online linear-quadratic control in a known system subject to adversarial disturbances. Existing regret bounds for this setting scale as √T unless strong stochastic assumptions are imposed on the disturbance process. We give the first algorithm with logarithmic regret for arbitrary adversarial disturbance sequences, provided the state and control costs are given by known quadratic functions. Our algorithm and analysis use a characterization for the optimal offline control law to reduce the online control problem to (delayed) online learning with approximate advantage functions. Compared to previous techniques, our approach does not need to control movement costs for the iterates, leading to logarithmic regret.