# Adversarial Tracking Control via Strongly Adaptive Online Learning with Memory

arXiv: https://arxiv.org/abs/2102.01623 · HTML: https://mlsanity.com/paper/2102.01623/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 65 references that are in the map.
- First posted on arXiv 2 Feb 2021.

## Builds on (most cited first, 30 of 32)

- [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)
- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Online Learning under Delayed Feedback](https://mlsanity.com/paper/1306.0686/) (2013)
- [Coin Betting and Parameter-Free Online Learning](https://mlsanity.com/paper/1602.04128/) (2016)
- [Black-Box Reductions for Parameter-free Online Learning in Banach Spaces](https://mlsanity.com/paper/1802.06293/) (2018)
- [Strongly Adaptive Online Learning](https://mlsanity.com/paper/1502.07073/) (2015)
- [Online Optimization : Competing with Dynamic Comparators](https://mlsanity.com/paper/1501.06225/) (2015)
- [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)
- [Lipschitz and Comparator-Norm Adaptivity in Online Learning](https://mlsanity.com/paper/2002.12242/) (2020)
- [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018)
- [Improved Strongly Adaptive Online Learning using Coin Betting](https://mlsanity.com/paper/1610.04578/) (2016)
- [Unconstrained Online Linear Learning in Hilbert Spaces: Minimax Algorithms and Normal Approximations](https://mlsanity.com/paper/1403.0628/) (2014)
- [Improved Dynamic Regret for Non-degenerate Functions](https://mlsanity.com/paper/1608.03933/) (2016)
- [An Optimal Algorithm for Adversarial Bandits with Arbitrary Delays](https://mlsanity.com/paper/1910.06054/) (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)
- [Smoothed Online Convex Optimization in High Dimensions via Online Balanced Descent](https://mlsanity.com/paper/1803.10366/) (2018)
- [Beyond Online Balanced Descent: An Optimal Algorithm for Smoothed Online Optimization](https://mlsanity.com/paper/1905.12776/) (2019)
- [Minimizing Dynamic Regret and Adaptive Regret Simultaneously](https://mlsanity.com/paper/2002.02085/) (2020)
- [The Power of Predictions in Online Control](https://mlsanity.com/paper/2006.07569/) (2020)
- [Adaptive Regret of Convex and Smooth Functions](https://mlsanity.com/paper/1904.11681/) (2019)
- [Making Non-Stochastic Control (Almost) as Easy as Stochastic](https://mlsanity.com/paper/2006.05910/) (2020)
- [Online Convex Optimization Using Predictions](https://mlsanity.com/paper/1504.06681/) (2015)
- [Online Gradient Boosting](https://mlsanity.com/paper/1506.04820/) (2015)
- [Dual Adaptivity: A Universal Algorithm for Minimizing the Adaptive Regret of Convex Functions](https://mlsanity.com/paper/1906.10851/) (2019)

## Built on by (most cited first, 14 of 14)

- [Optimal Stochastic Non-smooth Non-convex Optimization through Online-to-Non-convex Conversion](https://mlsanity.com/paper/2302.03775/) (2023)
- [Non-stationary Online Learning with Memory and Non-stochastic Control](https://mlsanity.com/paper/2102.03758/) (2021)
- [PDE-Based Optimal Strategy for Unconstrained Online Learning](https://mlsanity.com/paper/2201.07877/) (2022)
- [Exploiting the Curvature of Feasible Sets for Faster Projection-Free Online Learning](https://mlsanity.com/paper/2205.11470/) (2022)
- [Optimal Comparator Adaptive Online Learning with Switching Cost](https://mlsanity.com/paper/2205.06846/) (2022)
- [Adaptive Gradient Methods with Local Guarantees](https://mlsanity.com/paper/2203.01400/) (2022)
- [Smoothed Online Convex Optimization Based on Discounted-Normal-Predictor](https://mlsanity.com/paper/2205.00741/) (2022)
- [Efficient Online Learning with Memory via Frank-Wolfe Optimization: Algorithms with Bounded Dynamic Regret and Applications to Control](https://mlsanity.com/paper/2301.00497/) (2023)
- [Predictive Linear Online Tracking for Unknown Targets](https://mlsanity.com/paper/2402.10036/) (2024)
- [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)
- [Parameter-free Dynamic Regret: Time-varying Movement Costs, Delayed Feedback, and Memory](https://mlsanity.com/paper/2602.06902/) (2026)
- [Smoothed Online Optimization for Target Tracking: Robust and Learning-Augmented Algorithms](https://mlsanity.com/paper/2509.05930/) (2025)
- [Self-Adaptive Learning and Model Predictive Control for Tracking Unknown Dynamics with No Regret](https://mlsanity.com/paper/2607.26370/) (2026)

## Abstract (arXiv)

We consider the problem of tracking an adversarial state sequence in a linear dynamical system subject to adversarial disturbances and loss functions, generalizing earlier settings in the literature. To this end, we develop three techniques, each of independent interest. First, we propose a comparator-adaptive algorithm for online linear optimization with movement cost. Without tuning, it nearly matches the performance of the optimally tuned gradient descent in hindsight. Next, considering a related problem called online learning with memory, we construct a novel strongly adaptive algorithm that uses our first contribution as a building block. Finally, we present the first reduction from adversarial tracking control to strongly adaptive online learning with memory. Summarizing these individual techniques, we obtain an adversarial tracking controller with a strong performance guarantee even when the reference trajectory has a large range of movement.