Related papers: On the infinite-dimensional QR algorithm
Optimizing objective functions subject to constraints is fundamental in many real-world applications. However, these constraints are often not readily defined and must be inferred from expert agent behaviors, a problem known as Inverse…
In this paper, we present the QR Algorithm with Permutations that shows an improved convergence rate compared to the classical QR algorithm. We determine a bound for performance based on best instantaneous convergence, and develop low…
This note deals with the direct and inverse spectral analysis for a class of infinite band symmetric matrices. This class corresponds to operators arising from difference quations with usual and inner boundary conditions. We give a…
We consider policy gradient algorithms for the indefinite least squares stationary optimal control, e.g., linear-quadratic-regulator (LQR) with indefinite state and input penalization matrices. Such a setup has important applications in…
In this paper, we investigate a special class of quadratic-constrained quadratic programming (QCQP) with semi-definite constraints. Traditionally, since such a problem is non-convex and N-hard, the neural network (NN) is regarded as a…
It is an established fact that a finite difference operator approximates a derivative with a fixed algebraic rate of convergence. Nevertheless, we exhibit a new finite difference operator and prove it has spectral accuracy. Its rate of…
An efficient decoding algorithm named `divided decoder' is proposed in this paper. Divided decoding can be combined with any decoder using QR-decomposition and offers different pairs of performance and complexity. Divided decoding provides…
We consider the problem of learning a linear operator $\theta$ between two Hilbert spaces from empirical observations, which we interpret as least squares regression in infinite dimensions. We show that this goal can be reformulated as an…
The goal of this paper is to investigate new and simple convergence analysis of dynamic programming for linear quadratic regulator problem of discrete-time linear time-invariant systems. In particular, bounds on errors are given in terms of…
We consider Kramers-Fokker-Planck operators with general degenerate coefficients. We prove semiclassical hypocoercivity estimates for a large class of such operators. Then, we manage to prove Eyring-Kramers formulas for the bottom of the…
Inverse spectral problem for a self-adjoint differential operator, which is the sum of the operator of the third derivative on a finite interval and of the operator of multiplication by a real function (potential), is solved. Closed system…
Solving convex Semi-Infinite Programming (SIP) problems is challenging when the separation problem, i.e., the problem of finding the most violated constraint, is computationally hard. We propose to tackle this difficulty by solving the…
In this paper, we consider a class of nonconvex complex quadratic programming (CQP) problems, which find a broad spectrum of signal processing applications. By using the polar coordinate representations of the complex variables, we first…
The technique of semidefinite programming (SDP) relaxation can be used to obtain a nontrivial bound on the optimal value of a nonconvex quadratically constrained quadratic program (QCQP). We explore concave quadratic inequalities that hold…
In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…
We propose and analyse a class of analytically solvable models of quantum reinforcement learning (QRL), formulated as finite-horizon Markov decision processes in finite-dimensional Hilbert spaces. The models are built around a…
We consider a class of quasi-variational inequalities (QVIs) for adaptive image restoration, where the adaptivity is described via solution-dependent constraint sets. In previous work we studied both theoretical and numerical issues. While…
The application of quantum computation to accelerate machine learning algorithms is one of the most promising areas of research in quantum algorithms. In this paper, we explore the power of quantum learning algorithms in solving an…
We show that the problem of designing a quantum information error correcting procedure can be cast as a bi-convex optimization problem, iterating between encoding and recovery, each being a semidefinite program. For a given encoding…
We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought…