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Found 16 papers, 1 papers with code
State space models, emergence, and ergodicity: How many parameters are needed for stable predictions?
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.
A Short Information-Theoretic Analysis of Linear Auto-Regressive Learning
In this note, we give a short information-theoretic proof of the consistency of the Gaussian maximum likelihood estimator in linear auto-regressive models.
Finite Sample Analysis for a Class of Subspace Identification Methods
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.
Active Learning for Control-Oriented Identification of Nonlinear Systems
Model-based reinforcement learning is an effective approach for controlling an unknown system.
Rate-Optimal Non-Asymptotics for the Quadratic Prediction Error Method
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.
Sharp Rates in Dependent Learning Theory: Avoiding Sample Size Deflation for the Square Loss
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 $p\in [2,\infty]$.
A Tutorial on the Non-Asymptotic Theory of System Identification
This tutorial serves as an introduction to recently developed non-asymptotic methods in the theory of -- mainly linear -- system identification.
The Fundamental Limitations of Learning Linear-Quadratic Regulators
We present a local minimax lower bound on the excess cost of designing a linear-quadratic controller from offline data.
A note on the smallest eigenvalue of the empirical covariance of causal Gaussian processes
We present a simple proof for bounding the smallest eigenvalue of the empirical covariance in a causal Gaussian process.
Statistical Learning Theory for Control: A Finite Sample Perspective
This tutorial survey provides an overview of recent non-asymptotic advances in statistical learning theory as relevant to control and system identification.
Learning with little mixing
We study square loss in a realizable time-series framework with martingale difference noise.
How are policy gradient methods affected by the limits of control?
We study stochastic policy gradient methods from the perspective of control-theoretic limitations.
Learning to Control Linear Systems can be Hard
In this paper, we study the statistical difficulty of learning to control linear systems.
Single Trajectory Nonparametric Learning of Nonlinear Dynamics
Given a single trajectory of a dynamical system, we analyze the performance of the nonparametric least squares estimator (LSE).
Regret Lower Bounds for Learning Linear Quadratic Gaussian Systems
TWe establish regret lower bounds for adaptively controlling an unknown linear Gaussian system with quadratic costs.
On Uninformative Optimal Policies in Adaptive LQR with Unknown B-Matrix
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).
