# Minimax Lower Bounds for H_∞-Norm Estimation

arXiv: https://arxiv.org/abs/1809.10855 · HTML: https://mlsanity.com/paper/1809.10855/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2018.

## Built on by (most cited first, 4 of 4)

- [Global Convergence of Direct Policy Search for State-Feedback H_∞ Robust Control: A Revisit of Nonsmooth Synthesis with Goldstein Subdifferential](https://mlsanity.com/paper/2210.11577/) (2022)
- [Model-Free μ Synthesis via Adversarial Reinforcement Learning](https://mlsanity.com/paper/2111.15537/) (2021)
- [Finite Sample Frequency Domain Identification](https://mlsanity.com/paper/2404.01100/) (2024)
- [Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem](https://mlsanity.com/paper/2411.15972/) (2024)

## Abstract (arXiv)

The problem of estimating the H_∞-norm of an LTI system from noisy input/output measurements has attracted recent attention as an alternative to parameter identification for bounding unmodeled dynamics in robust control. In this paper, we study lower bounds for H_∞-norm estimation under a query model where at each iteration the algorithm chooses a bounded input signal and receives the response of the chosen signal corrupted by white noise. We prove that when the underlying system is an FIR filter, H_∞-norm estimation is no more efficient than model identification for passive sampling. For active sampling, we show that norm estimation is at most a factor of logr more sample efficient than model identification, where r is the length of the filter. We complement our theoretical results with experiments which demonstrate that a simple non-adaptive estimator of the norm is competitive with state-of-the-art adaptive norm estimation algorithms.