Related papers: Sample Complexity Lower Bounds for Linear System I…
One of the central issues in the hidden subgroup problem is to bound the sample complexity, i.e., the number of identical samples of coset states sufficient and necessary to solve the problem. In this paper, we present general bounds for…
This paper proposes a frequency-domain system identification method for learning low-order systems. The identification problem is formulated as the minimization of the l2 norm between the identified and measured frequency responses, with…
Sensitivity measures how much the output of an algorithm changes, in terms of Hamming distance, when part of the input is modified. While approximation algorithms with low sensitivity have been developed for many problems, no sensitivity…
Recently, there has been significant progress in understanding reinforcement learning in discounted infinite-horizon Markov decision processes (MDPs) by deriving tight sample complexity bounds. However, in many real-world applications, an…
This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation…
In this work, we consider the problem of identifying an unknown linear dynamical system given a finite hypothesis class. In particular, we analyze the effect of the excitation input on the sample complexity of identifying the true system…
We investigate the problem of establishing finite-time probabilistic safety guarantees for discrete-time stochastic dynamical systems subject to unknown disturbance distributions, using barrier certificate methods. Our approach develops a…
Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…
The quantum statistics mechanism is very powerful for investigating the equilibrium states and the phase transitions in complex spin disorder systems. The spin disorder systems act as an interdisciplinary platform for solving the optimum…
In this paper, we consider the problem of replicable realizable PAC learning. We construct a particularly hard learning problem and show a sample complexity lower bound with a close to $(\log|H|)^{3/2}$ dependence on the size of the…
We derive an information-theoretic lower bound for sample complexity in sparse recovery problems where inputs can be chosen sequentially and adaptively. This lower bound is in terms of a simple mutual information expression and unifies many…
In this work, we consider the controllability of a discrete-time linear dynamical system with sparse control inputs. Sparsity constraints on the input arises naturally in networked systems, where activating each input variable adds to the…
In this paper, we study the statistical difficulty of learning to control linear systems. We focus on two standard benchmarks, the sample complexity of stabilization, and the regret of the online learning of the Linear Quadratic Regulator…
A fundamental problem in adversarial machine learning is to quantify how much training data is needed in the presence of evasion attacks. In this paper we address this issue within the framework of PAC learning, focusing on the class of…
Metric learning seeks a transformation of the feature space that enhances prediction quality for the given task at hand. In this work we provide PAC-style sample complexity rates for supervised metric learning. We give matching lower- and…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…
In temporal planning, many different temporal network formalisms are used to model real world situations. Each of these formalisms has different features which affect how easy it is to determine whether the underlying network of temporal…
System identification is a key enabling component for the implementation of quantum technologies, including quantum control. In this paper, we consider the class of passive linear input-output systems, and investigate several basic…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
This work establishes a new upper bound on the number of samples sufficient for PAC learning in the realizable case. The bound matches known lower bounds up to numerical constant factors. This solves a long-standing open problem on the…