Related papers: Optimizing quantum optimization algorithms via fas…
In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is…
Variational quantum algorithms are a leading candidate for early applications on noisy intermediate-scale quantum computers. These algorithms depend on a classical optimization outer-loop that minimizes some function of a parameterized…
This paper considers a finite-sum optimization problem under first-order queries and investigates the benefits of strategic querying on stochastic gradient-based methods compared to uniform querying strategy. We first introduce Oracle…
Quantum kernel methods are among the leading candidates for achieving quantum advantage in supervised learning. A key bottleneck is the cost of inference: evaluating a trained model on new data requires estimating a weighted sum…
The search task is one of the most difficult when it comes to execution speed, and reducing the latter is important both when working with large data and with small samples, if they need to be processed frequently and in a limited time.…
Optimization theory has been widely studied in academia and finds a large variety of applications in industry. The different optimization models in their discrete and/or continuous settings have catered to a rich source of research…
Gradient-based minimax optimal algorithms have greatly promoted the development of continuous optimization and machine learning. One seminal work due to Yurii Nesterov [Nes83a] established $\tilde{\mathcal{O}}(\sqrt{L/\mu})$ gradient…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we make two main contributions. First, we…
Engineering the Hamiltonian of a quantum system is fundamental to the design of quantum systems. Automating Hamiltonian design through gradient-based optimization can dramatically accelerate this process. However, computing the gradients of…
In this paper we propose two proximal gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either…
We adapt the gradient sampling algorithm to the local scoring algorithm to solve complex estimation problems based on an optimization of an objective function. This overcomes non-differentiability and non-smoothness of the objective…
Gradient-based iterative optimization methods are the workhorse of modern machine learning. They crucially rely on careful tuning of parameters like learning rate and momentum. However, one typically sets them using heuristic approaches…
Functions are a fundamental object in mathematics, with countless applications to different fields, and are usually classified based on certain properties, given their domains and images. An important property of a real-valued function is…
Variational quantum algorithms (VQAs) provide a promising approach to achieving quantum advantage for practical problems on near-term noisy intermediate-scale quantum (NISQ) devices. Thus far, most studies on VQAs have focused on…
The quantum approximate optimization algorithm (QAOA), as a hybrid quantum/classical algorithm, has received much interest recently. QAOA can also be viewed as a variational ansatz for quantum control. However, its direct application to…
Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…
Advances in numerical optimization have supported breakthroughs in several areas of signal processing. This paper focuses on the recent enhanced variants of the proximal gradient numerical optimization algorithm, which combine quasi-Newton…
Universal methods for optimization are designed to achieve theoretically optimal convergence rates without any prior knowledge of the problem's regularity parameters or the accurarcy of the gradient oracle employed by the optimizer. In this…
A novel class of hybrid quantum-classical algorithms based on the variational approach have recently emerged from separate proposals addressing, for example, quantum chemistry and combinatorial problems. These algorithms provide an…