Related papers: On the infinite-dimensional QR algorithm
In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…
In coming up with solutions to real-world problems, humans implicitly adhere to constraints that are too numerous and complex to be specified completely. However, reinforcement learning (RL) agents need these constraints to learn the…
State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are…
This paper develops a mathematical theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples…
Under conditions that prevent tangential intersection, we prove quadratic convergence of a projection algorithm for the feasibility problem of finding a point in the intersection of a smooth curve and line in $\mathbb{R}^2$. This nonconvex…
This paper studies the inference problem in quantile regression (QR) for a large sample size $n$ but under a limited memory constraint, where the memory can only store a small batch of data of size $m$. A natural method is the na\"ive…
With the beginning of the noisy intermediate-scale quantum (NISQ) era, a quantum neural network (QNN) has recently emerged as a solution for several specific problems that classical neural networks cannot solve. Moreover, a quantum…
A method is presented for solving the discrete-time finite-horizon Linear Quadratic Regulator (LQR) problem subject to auxiliary linear equality constraints, such as fixed end-point constraints. The method explicitly determines an affine…
In this paper we study a class of quadratic operators named by Volterra operators on infinite dimensional space. We prove that such operators have infinitely many fixed points and the set of Volterra operators forms a convex compact set. In…
This paper investigates the convergence properties of spectral algorithms -- a class of regularization methods originating from inverse problems -- under covariate shift. In this setting, the marginal distributions of inputs differ between…
Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…
The thesis deals with Quantum Algorithms for solving Hard Constrained Optimization Problems. It shows how quantum computers can solve difficult everyday problems such as finding the best schedule for social workers or the path of a robot…
We study the expressibility and learnability of convex optimization solution functions and their multi-layer architectural extension. The main results are: \emph{(1)} the class of solution functions of linear programming (LP) and quadratic…
Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an…
Operator eigenvalue problems play a critical role in various scientific fields and engineering applications, yet numerical methods are hindered by the curse of dimensionality. Recent deep learning methods provide an efficient approach to…
Fault-tolerant schemes can use error correction to make a quantum computation arbitrarily ac- curate, provided that errors per physical component are smaller than a certain threshold and in- dependent of the computer size. However in…
Integer semidefinite programming (ISDP) has recently gained attention due to its connection to binary quadratically constrained quadratic programs (BQCQPs), which can be exactly reformulated as binary semidefinite programs (BSDPs). However,…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
We investigate the possibility of solving continuous non-convex optimization problems using a network of interacting quantum optical oscillators. We propose a native encoding of continuous variables in analog signals associated with the…
We consider the problem of operator-valued kernel learning and investigate the possibility of going beyond the well-known separable kernels. Borrowing tools and concepts from the field of quantum computing, such as partial trace and…