# On the relation between dynamic regret and closed-loop stability

arXiv: https://arxiv.org/abs/2209.05964 · HTML: https://mlsanity.com/paper/2209.05964/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2022.

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

- [Implications of Regret on Stability of Linear Dynamical Systems](https://mlsanity.com/paper/2211.07411/) (2022)
- [Regret Analysis of Distributed Online Control for LTI Systems with Adversarial Disturbances](https://mlsanity.com/paper/2310.03206/) (2023)
- [A Spectral Filtering Approach to Regret Analysis of Distributed Online Control for Linear Dynamical Systems](https://mlsanity.com/paper/2608.02375/) (2026)

## Abstract (arXiv)

In this work, we study the relations between bounded dynamic regret and the classical notion of asymptotic stability for the case of a priori unknown and time-varying cost functions. In particular, we show that bounded dynamic regret implies asymptotic stability of the optimal steady state for a constant cost function. For the case of an asymptotically stable closed loop, we first derive a necessary condition for achieving bounded dynamic regret. Then, given some additional assumptions on the system and the cost functions, we also provide a sufficient condition ensuring bounded dynamic regret. Our results are illustrated by examples.