Related papers: Linear Systems can be Hard to Learn
In the recent years, branch-and-cut algorithms have been the target of data-driven approaches designed to enhance the decision making in different phases of the algorithm such as branching, or the choice of cutting planes (cuts). In…
It is becoming increasingly important to understand the vulnerability of machine learning models to adversarial attacks. In this paper we study the feasibility of robust learning from the perspective of computational learning theory,…
Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…
An effective weighting scheme for training samples is essential for learning tasks. Numerous weighting schemes have been proposed. Some schemes take the easy-first mode, whereas some others take the hard-first one. Naturally, an interesting…
This paper studies the problem of, given the structure of a linear-time invariant system and a set of possible inputs, finding the smallest subset of input vectors that ensures system's structural controllability. We refer to this problem…
A complete structure-preserving learning scheme for single-input/single-output (SISO) linear port-Hamiltonian systems is proposed. The construction is based on the solution, when possible, of the unique identification problem for these…
We study the problem of identifying the dynamics of a linear system when one has access to samples generated by a similar (but not identical) system, in addition to data from the true system. We use a weighted least squares approach and…
We determine the complexity of counting models of bounded size of specifications expressed in Linear-time Temporal Logic. Counting word models is #P-complete, if the bound is given in unary, and as hard as counting accepting runs of…
Given a linear system, we consider the problem of finding a small set of variables to affect with an input so that the resulting system is controllable. We show that this problem is NP-hard; indeed, we show that even approximating the…
Learning monotonic models with respect to a subset of the inputs is a desirable feature to effectively address the fairness, interpretability, and generalization issues in practice. Existing methods for learning monotonic neural networks…
The scenario approach is widely used in robust control system design and chance-constrained optimization, maintaining convexity without requiring assumptions about the probability distribution of uncertain parameters. However, the approach…
The impossibility of simultaneously cloning non-orthogonal states lies at the foundations of quantum theory. Even when allowing for approximation errors, cloning an arbitrary unknown pure state requires as many initial copies as needed to…
Distinguishability takes a crucial rule in studying observability of hybrid system such as switched system. Recently, for two linear systems, Lou and Si gave a condition not only necessary but also sufficient to the distinguishability of…
There has been a recent interest in imitation learning methods that are guaranteed to produce a stabilizing control law with respect to a known system. Work in this area has generally considered linear systems and controllers, for which…
The problem of learning the structure of a high dimensional graphical model from data has received considerable attention in recent years. In many applications such as sensor networks and proteomics it is often expensive to obtain samples…
In many sampled-data applications, observers are designed based on approximately discretized models of continuous-time systems, where usually only the discretized system is analyzed in terms of its detectability. In this paper, we show that…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
This paper considers the Linear Quadratic Regulator problem for linear systems with unknown dynamics, a central problem in data-driven control and reinforcement learning. We propose a method that uses data to directly return a controller…
This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly…