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Optimization is offered as an objective approach to resolving complex, real-world decisions involving uncertainty and conflicting interests. It drives business strategies as well as public policies and, increasingly, lies at the heart of…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
We study the optimization landscape and the stability properties of training problems with squared loss for neural networks and general nonlinear conic approximation schemes. It is demonstrated that, if a nonlinear conic approximation…
Efficient solving of an unseen optimization problem is related to appropriate selection of an optimization algorithm and its hyper-parameters. For this purpose, automated algorithm performance prediction should be performed that in most…
We present a new modeling paradigm for optimization that we call random field optimization. Random fields are a powerful modeling abstraction that aims to capture the behavior of random variables that live on infinite-dimensional spaces…
Training neural networks involves solving large-scale non-convex optimization problems. This task has long been believed to be extremely difficult, with fear of local minima and other obstacles motivating a variety of schemes to improve…
The variational quantum algorithm (VQA) with a parametrized quantum circuit is widely applicable to near-term quantum computing, but its fundamental issues that limit optimization performance have been reported in the literature. For…
There is a strong interest in optimal manipulating of quantum systems by external controls. Traps are controls which are optimal only locally but not globally. If they exist, they can be serious obstacles to the search of globally optimal…
A problem of the erroneous duality gap caused by the presence of symmetries is solved in this paper utilizing point group theory. The optimization problems are first divided into two classes based on their predisposition to suffer from this…
Quantum annealing is a computational paradigm in which optimisation problems are mapped onto the energy landscape of an interacting quantum system and explored through its dynamical evolution. By continuously transforming a simple initial…
%% Text of abstract The process of identifying the most suitable optimization algorithm for a specific problem, referred to as algorithm selection (AS), entails training models that leverage problem landscape features to forecast algorithm…
Machine learning algorithms have been used widely in various applications and areas. To fit a machine learning model into different problems, its hyper-parameters must be tuned. Selecting the best hyper-parameter configuration for machine…
Optimization methods play a crucial role in modern machine learning, powering the remarkable empirical achievements of deep learning models. These successes are even more remarkable given the complex non-convex nature of the loss landscape…
Equivariant neural networks have proven to be effective for tasks with known underlying symmetries. However, optimizing equivariant networks can be tricky and best training practices are less established than for standard networks. In…
We analyze the optimization landscapes of deep learning with wide networks. We highlight the importance of constraints for such networks and show that constraint -- as well as unconstraint -- empirical-risk minimization over such networks…
Optimization drives advances in quantum science and machine learning, yet most generative models aim to mimic data rather than to discover optimal answers to challenging problems. Here we present a variational generative optimization…
The problem of parameterization is often central to the effective deployment of nature-inspired algorithms. However, finding the optimal set of parameter values for a combination of problem instance and solution method is highly…
Variational quantum algorithms are viewed as promising candidates for demonstrating quantum advantage on near-term devices. These approaches typically involve the training of parameterized quantum circuits through a classical optimization…
The performance of variational quantum algorithms relies on the success of using quantum and classical computing resources in tandem. Here, we study how these quantum and classical components interrelate. In particular, we focus on…
In recent years, quantum, quantum-inspired, and hybrid algorithms are increasingly showing promise for solving software engineering optimization problems. However, best-intended practices for conducting empirical studies have not yet well…