no code implementations • 20 Sep 2024 • Ingvar Ziemann, Nikolai Matni, George J. Pappas

For this situation, we show that there exists no learner using a linear filter which can succesfully learn the random walk unless the filter length exceeds a certain threshold depending on the effective memory length and horizon of the problem.

no code implementations • 10 Sep 2024 • Ingvar Ziemann

In this note, we give a short information-theoretic proof of the consistency of the Gaussian maximum likelihood estimator in linear auto-regressive models.

no code implementations • 26 Apr 2024 • Jiabao He, Ingvar Ziemann, Cristian R. Rojas, Håkan Hjalmarsson

While subspace identification methods (SIMs) are appealing due to their simple parameterization for MIMO systems and robust numerical realizations, a comprehensive statistical analysis of SIMs remains an open problem, especially in the non-asymptotic regime.

no code implementations • 13 Apr 2024 • Bruce D. Lee, Ingvar Ziemann, George J. Pappas, Nikolai Matni

Model-based reinforcement learning is an effective approach for controlling an unknown system.

no code implementations • 11 Apr 2024 • Charis Stamouli, Ingvar Ziemann, George J. Pappas

We study the quadratic prediction error method -- i. e., nonlinear least squares -- for a class of time-varying parametric predictor models satisfying a certain identifiability condition.

no code implementations • 8 Feb 2024 • Ingvar Ziemann, Stephen Tu, George J. Pappas, Nikolai Matni

In this work, we study statistical learning with dependent ($\beta$-mixing) data and square loss in a hypothesis class $\mathscr{F}\subset L_{\Psi_p}$ where $\Psi_p$ is the norm $\|f\|_{\Psi_p} \triangleq \sup_{m\geq 1} m^{-1/p} \|f\|_{L^m} $ for some $p\in [2,\infty]$.

no code implementations • 7 Sep 2023 • Ingvar Ziemann, Anastasios Tsiamis, Bruce Lee, Yassir Jedra, Nikolai Matni, George J. Pappas

This tutorial serves as an introduction to recently developed non-asymptotic methods in the theory of -- mainly linear -- system identification.

no code implementations • 27 Mar 2023 • Bruce D. Lee, Ingvar Ziemann, Anastasios Tsiamis, Henrik Sandberg, Nikolai Matni

We present a local minimax lower bound on the excess cost of designing a linear-quadratic controller from offline data.

no code implementations • 19 Dec 2022 • Ingvar Ziemann

We present a simple proof for bounding the smallest eigenvalue of the empirical covariance in a causal Gaussian process.

no code implementations • 12 Sep 2022 • Anastasios Tsiamis, Ingvar Ziemann, Nikolai Matni, George J. Pappas

This tutorial survey provides an overview of recent non-asymptotic advances in statistical learning theory as relevant to control and system identification.

1 code implementation • 16 Jun 2022 • Ingvar Ziemann, Stephen Tu

We study square loss in a realizable time-series framework with martingale difference noise.

no code implementations • 14 Jun 2022 • Ingvar Ziemann, Anastasios Tsiamis, Henrik Sandberg, Nikolai Matni

We study stochastic policy gradient methods from the perspective of control-theoretic limitations.

no code implementations • 27 May 2022 • Anastasios Tsiamis, Ingvar Ziemann, Manfred Morari, Nikolai Matni, George J. Pappas

In this paper, we study the statistical difficulty of learning to control linear systems.

no code implementations • 16 Feb 2022 • Ingvar Ziemann, Henrik Sandberg, Nikolai Matni

Given a single trajectory of a dynamical system, we analyze the performance of the nonparametric least squares estimator (LSE).

no code implementations • 5 Jan 2022 • Ingvar Ziemann, Henrik Sandberg

TWe establish regret lower bounds for adaptively controlling an unknown linear Gaussian system with quadratic costs.

no code implementations • 18 Nov 2020 • Ingvar Ziemann, Henrik Sandberg

After defining the intrinsic notion of an uninformative optimal policy in terms of a singularity condition for Fisher information we obtain local minimax regret lower bounds for such uninformative instances of LQR by appealing to van Trees' inequality (Bayesian Cram\'er-Rao) and a representation of regret in terms of a quadratic form (Bellman error).

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