Related papers: Quantum Algorithms for Structured Prediction

In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…

Quantum machine learning provides a fundamentally different approach to analyzing data. However, many interesting datasets are too complex for currently available quantum computers. Present quantum machine learning applications usually…

We consider the problem of minimizing a continuous function given quantum access to a stochastic gradient oracle. We provide two new methods for the special case of minimizing a Lipschitz convex function. Each method obtains a dimension…

Minimax optimization problems have attracted significant attention in recent years due to their widespread application in numerous machine learning models. To solve the minimax problem, a wide variety of stochastic optimization methods have…

We propose a family of nonconvex optimization algorithms that are able to save gradient and negative curvature computations to a large extent, and are guaranteed to find an approximate local minimum with improved runtime complexity. At the…

The paper considers the problem of network-based computation of global minima in smooth nonconvex optimization problems. It is known that distributed gradient-descent-type algorithms can achieve convergence to the set of global minima by…

This paper considers the projection-free sparse convex optimization problem for the vector domain and the matrix domain, which covers a large number of important applications in machine learning and data science. For the vector domain…

Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…

Many applications in automated auditing and the analysis and consistency check of financial documents can be formulated in part as the subset sum problem: Given a set of numbers and a target sum, find the subset of numbers that sums up to…

A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…

Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the model selection…

The general perception is that kernel methods are not scalable, and neural nets are the methods of choice for nonlinear learning problems. Or have we simply not tried hard enough for kernel methods? Here we propose an approach that scales…

Quantum machines are among the most promising technologies expected to provide significant improvements in the following years. However, bridging the gap between real-world applications and their implementation on quantum hardware is still…

We study the foundations of variational inference, which frames posterior inference as an optimisation problem, for probabilistic programming. The dominant approach for optimisation in practice is stochastic gradient descent. In particular,…

Gaussian Process Regression is a well-known machine learning technique for which several quantum algorithms have been proposed. We show here that in a wide range of scenarios these algorithms show no exponential speedup. We achieve this by…

We propose a novel stochastic gradient descent method for solving linear least squares problems with partially observed data. Our method uses submatrices indexed by a randomly selected pair of row and column index sets to update the iterate…

The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…

We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), Ising spin glasses ($p$-spin model), and $k$-local…

We consider Markov Decision Problems defined over continuous state and action spaces, where an autonomous agent seeks to learn a map from its states to actions so as to maximize its long-term discounted accumulation of rewards. We address…

With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used…