# Adaptive Regret for Control of Time-Varying Dynamics

arXiv: https://arxiv.org/abs/2007.04393 · HTML: https://mlsanity.com/paper/2007.04393/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2020.

## Built on by (most cited first, 30 of 38)

- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
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- [Non-stationary Online Learning with Memory and Non-stochastic Control](https://mlsanity.com/paper/2102.03758/) (2021)
- [Adversarial Tracking Control via Strongly Adaptive Online Learning with Memory](https://mlsanity.com/paper/2102.01623/) (2021)
- [Online Control of Unknown Time-Varying Dynamical Systems](https://mlsanity.com/paper/2202.07890/) (2022)
- [Error-quantified Conformal Inference for Time Series](https://mlsanity.com/paper/2502.00818/) (2025)
- [Deluca -- A Differentiable Control Library: Environments, Methods, and Benchmarking](https://mlsanity.com/paper/2102.09968/) (2021)
- [Regret-optimal Estimation and Control](https://mlsanity.com/paper/2106.12097/) (2021)
- [Competitive Control](https://mlsanity.com/paper/2107.13657/) (2021)
- [Provable Regret Bounds for Deep Online Learning and Control](https://mlsanity.com/paper/2110.07807/) (2021)
- [Smoothed Online Convex Optimization Based on Discounted-Normal-Predictor](https://mlsanity.com/paper/2205.00741/) (2022)
- [Optimal Dynamic Regret in LQR Control](https://mlsanity.com/paper/2206.09257/) (2022)
- [Best of Both Worlds in Online Control: Competitive Ratio and Policy Regret](https://mlsanity.com/paper/2211.11219/) (2022)
- [Online Optimization with Feedback Delay and Nonlinear Switching Cost](https://mlsanity.com/paper/2111.00095/) (2021)
- [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)
- [A Regret Minimization Approach to Multi-Agent Control](https://mlsanity.com/paper/2201.13288/) (2022)
- [A Nonstochastic Control Approach to Optimization](https://mlsanity.com/paper/2301.07902/) (2023)
- [Adaptive Conformal Inference by Particle Filtering under Hidden Markov Models](https://mlsanity.com/paper/2411.01558/) (2024)
- [Stable Online Control of Linear Time-Varying Systems](https://mlsanity.com/paper/2104.14134/) (2021)
- [Stochastic Multi-armed Bandits with Non-stationary Rewards Generated by a Linear Dynamical System](https://mlsanity.com/paper/2204.05782/) (2022)
- [Implications of Regret on Stability of Linear Dynamical Systems](https://mlsanity.com/paper/2211.07411/) (2022)
- [Instance-Conditional Timescales of Decay for Non-Stationary Learning](https://mlsanity.com/paper/2212.05908/) (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)
- [On the Computational Efficiency of Adaptive and Dynamic Regret Minimization](https://mlsanity.com/paper/2207.00646/) (2022)
- [Regret Analysis of Distributed Online Control for LTI Systems with Adversarial Disturbances](https://mlsanity.com/paper/2310.03206/) (2023)
- [Online Stackelberg Optimization via Nonlinear Control](https://mlsanity.com/paper/2406.18805/) (2024)
- [Online conformal inference with retrospective adjustment for faster adaptation to distribution shift](https://mlsanity.com/paper/2511.04275/) (2025)
- [Adaptive Bayesian Online Learning via Expert Aggregation](https://mlsanity.com/paper/2607.20239/) (2026)

## Abstract (arXiv)

We consider the problem of online control of systems with time-varying linear dynamics. This is a general formulation that is motivated by the use of local linearization in control of nonlinear dynamical systems. To state meaningful guarantees over changing environments, we introduce the metric of it adaptive regret to the field of control. This metric, originally studied in online learning, measures performance in terms of regret against the best policy in hindsight on it any interval in time, and thus captures the adaptation of the controller to changing dynamics. Our main contribution is a novel efficient meta-algorithm: it converts a controller with sublinear regret bounds into one with sublinear it adaptive regret bounds in the setting of time-varying linear dynamical systems. The main technical innovation is the first adaptive regret bound for the more general framework of online convex optimization with memory. Furthermore, we give a lower bound showing that our attained adaptive regret bound is nearly tight for this general framework.