# Optimistic Online Non-stochastic Control via FTRL

arXiv: https://arxiv.org/abs/2404.03309 · HTML: https://mlsanity.com/paper/2404.03309/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 51 references that are in the map.
- First posted on arXiv 4 Apr 2024.

## Builds on (most cited first, 30 of 35)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [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 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)
- [Online Learning with Optimism and Delay](https://mlsanity.com/paper/2106.06885/) (2021)
- [The Power of Predictions in Online Control](https://mlsanity.com/paper/2006.07569/) (2020)
- [Perturbation-based Regret Analysis of Predictive Control in Linear Time Varying Systems](https://mlsanity.com/paper/2106.10497/) (2021)
- [Making Non-Stochastic Control (Almost) as Easy as Stochastic](https://mlsanity.com/paper/2006.05910/) (2020)
- [On the Regret Analysis of Online LQR Control with Predictions](https://mlsanity.com/paper/2102.01309/) (2021)
- [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)
- [Bounded-Regret MPC via Perturbation Analysis: Prediction Error, Constraints, and Nonlinearity](https://mlsanity.com/paper/2210.12312/) (2022)
- [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)
- [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)
- [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)
- [Online Submodular Maximization via Online Convex Optimization](https://mlsanity.com/paper/2309.04339/) (2023)
- [On the Regret of H∞ Control](https://mlsanity.com/paper/2203.16237/) (2022)

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

- [On the Dynamic Regret of Following the Regularized Leader: Optimism with History Pruning](https://mlsanity.com/paper/2505.22899/) (2025)
- [Optimistic Learning for Communication Networks](https://mlsanity.com/paper/2504.03499/) (2025)
- [Constrained Online Convex Optimization with Memory and Predictions](https://mlsanity.com/paper/2603.21375/) (2026)

## Abstract (arXiv)

This paper brings the concept of ``optimism" to the new and promising framework of online Non-stochastic Control (NSC). Namely, we study how NSC can benefit from a prediction oracle of unknown quality responsible for forecasting future costs. The posed problem is first reduced to an optimistic learning with delayed feedback problem, which is handled through the Optimistic Follow the Regularized Leader (OFTRL) algorithmic family. This reduction enables the design of textttOptFTRL-C, the first Disturbance Action Controller (DAC) with optimistic policy regret bounds. These new bounds are commensurate with the oracle's accuracy, ranging from O(1) for perfect predictions to the order-optimal O(√T) even when all predictions fail. By addressing the challenge of incorporating untrusted predictions into online control, this work contributes to the advancement of the NSC framework and paves the way toward effective and robust learning-based controllers.