# Adaptive Online Non-stochastic Control

arXiv: https://arxiv.org/abs/2310.02261 · HTML: https://mlsanity.com/paper/2310.02261/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 41 references that are in the map.
- First posted on arXiv 2 Oct 2023.

## Builds on (most cited first, 29 of 29)

- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Online Control with Adversarial Disturbances](https://mlsanity.com/paper/1902.08721/) (2019)
- [Improper Learning for Non-Stochastic Control](https://mlsanity.com/paper/2001.09254/) (2020)
- [Online Learning with Switching Costs and Other Adaptive Adversaries](https://mlsanity.com/paper/1302.4387/) (2013)
- [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018)
- [The Nonstochastic Control Problem](https://mlsanity.com/paper/1911.12178/) (2019)
- [Logarithmic Regret for Adversarial Online Control](https://mlsanity.com/paper/2003.00189/) (2020)
- [Online Optimal Control with Linear Dynamics and Predictions: Algorithms and Regret Analysis](https://mlsanity.com/paper/1906.11378/) (2019)
- [Logarithmic Regret for Online Control](https://mlsanity.com/paper/1909.05062/) (2019)
- [Adaptive Regret for Control of Time-Varying Dynamics](https://mlsanity.com/paper/2007.04393/) (2020)
- [Non-stationary Online Learning with Memory and Non-stochastic Control](https://mlsanity.com/paper/2102.03758/) (2021)
- [The Power of Predictions in Online Control](https://mlsanity.com/paper/2006.07569/) (2020)
- [Making Non-Stochastic Control (Almost) as Easy as Stochastic](https://mlsanity.com/paper/2006.05910/) (2020)
- [Online Optimal Control with Affine Constraints](https://mlsanity.com/paper/2010.04891/) (2020)
- [Introduction to Online Control](https://mlsanity.com/paper/2211.09619/) (2022)
- [Non-Stochastic Control with Bandit Feedback](https://mlsanity.com/paper/2008.05523/) (2020)
- [Online Convex Optimization Using Predictions](https://mlsanity.com/paper/1504.06681/) (2015)
- [Adversarial Tracking Control via Strongly Adaptive Online Learning with Memory](https://mlsanity.com/paper/2102.01623/) (2021)
- [Robustness and Consistency in Linear Quadratic Control with Untrusted Predictions](https://mlsanity.com/paper/2106.09659/) (2021)
- [No-Regret Online Reinforcement Learning with Adversarial Losses and Transitions](https://mlsanity.com/paper/2305.17380/) (2023)
- [Optimism in Face of a Context: Regret Guarantees for Stochastic Contextual MDP](https://mlsanity.com/paper/2207.11126/) (2022)
- [Optimistic No-regret Algorithms for Discrete Caching](https://mlsanity.com/paper/2208.06414/) (2022)
- [Competitive Control with Delayed Imperfect Information](https://mlsanity.com/paper/2010.11637/) (2020)
- [Machine Learning for Mechanical Ventilation Control](https://mlsanity.com/paper/2102.06779/) (2021)
- [Competitive Control](https://mlsanity.com/paper/2107.13657/) (2021)
- [Best of Both Worlds in Online Control: Competitive Ratio and Policy Regret](https://mlsanity.com/paper/2211.11219/) (2022)
- [On the Regret of H∞ Control](https://mlsanity.com/paper/2203.16237/) (2022)
- [Online Nonstochastic Control with Adversarial and Static Constraints](https://mlsanity.com/paper/2302.02426/) (2023)
- [Online Caching with no Regret: Optimistic Learning via Recommendations](https://mlsanity.com/paper/2204.09345/) (2022)

## Built on by (most cited first, 3 of 3)

- [Optimistic Online Non-stochastic Control via FTRL](https://mlsanity.com/paper/2404.03309/) (2024)
- [Optimistic Learning for Communication Networks](https://mlsanity.com/paper/2504.03499/) (2025)
- [Smoothed Online Optimization for Target Tracking: Robust and Learning-Augmented Algorithms](https://mlsanity.com/paper/2509.05930/) (2025)

## Abstract (arXiv)

We tackle the problem of Non-stochastic Control (NSC) with the aim of obtaining algorithms whose policy regret is proportional to the difficulty of the controlled environment. Namely, we tailor the Follow The Regularized Leader (FTRL) framework to dynamical systems by using regularizers that are proportional to the actual witnessed costs. The main challenge arises from using the proposed adaptive regularizers in the presence of a state, or equivalently, a memory, which couples the effect of the online decisions and requires new tools for bounding the regret. Via new analysis techniques for NSC and FTRL integration, we obtain novel disturbance action controllers (DAC) with sub-linear data adaptive policy regret bounds that shrink when the trajectory of costs has small gradients, while staying sub-linear even in the worst case.