Related papers: Robust and efficient algorithms for high-dimension…
Motivated by broad applications in machine learning, we study the popular accelerated stochastic gradient descent (ASGD) algorithm for solving (possibly nonconvex) optimization problems. We characterize the finite-time performance of this…
In this paper, we study the convergence of the Adaptive Moment Estimation (Adam) algorithm under unconstrained non-convex smooth stochastic optimizations. Despite the widespread usage in machine learning areas, its theoretical properties…
Adaptive gradient algorithms perform gradient-based updates using the history of gradients and are ubiquitous in training deep neural networks. While adaptive gradient methods theory is well understood for minimization problems, the…
Variational quantum circuits characterise the state of a quantum system through the use of parameters that are optimised using classical optimisation procedures that typically rely on gradient information. The circuit-execution complexity…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
In this paper we introduce the Boosted Double-proximal Subgradient Algorithm (BDSA), a novel splitting algorithm designed to address general structured nonsmooth and nonconvex mathematical programs expressed as sums and differences of…
In order to exploit quantum advantages, quantum algorithms are indispensable for operating machine learning with quantum computers. We here propose an intriguing hybrid approach of quantum information processing for quantum linear…
Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…
We develop a framework for efficiently transforming certain approximation algorithms into differentially-private variants, in a black-box manner. Specifically, our results focus on algorithms A that output an approximation to a function f…
We propose an adaptive random quantum algorithm to obtain an optimized eigensolver. Specifically, we introduce a general method to parametrize and optimize the probability density function of a random number generator, which is the core of…
Combinatorial optimization with a smooth and convex objective function arises naturally in applications such as discrete mean-variance portfolio optimization, where assets must be traded in integer quantities. Although optimal solutions to…
Robust Markov Decision Processes (RMDPs) have recently been recognized as a valuable and promising approach to discovering a policy with creditable performance, particularly in the presence of a dynamic environment and estimation errors in…
We solve robot trajectory planning problems at industry-relevant scales. Our end-to-end solution integrates highly versatile random-key algorithms with model stacking and ensemble techniques, as well as path relinking for solution…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
One of the main challenges in drug discovery is to find molecules that bind specifically and strongly to their target protein while having minimal binding to other proteins. By predicting binding affinity, it is possible to identify the…
Research into optimisation for deep learning is characterised by a tension between the computational efficiency of first-order, gradient-based methods (such as SGD and Adam) and the theoretical efficiency of second-order, curvature-based…
Solving combinatorial optimization problems on current noisy quantum devices is currently being advocated for (and restricted to) binary polynomial optimization with equality constraints via quantum heuristic approaches. This is achieved…
We study a hybrid conditional gradient - smoothing algorithm (HCGS) for solving composite convex optimization problems which contain several terms over a bounded set. Examples of these include regularization problems with several norms as…
Despite the strong theoretical guarantees that variance-reduced finite-sum optimization algorithms enjoy, their applicability remains limited to cases where the memory overhead they introduce (SAG/SAGA), or the periodic full gradient…
Image recognition is one of the primary applications of machine learning algorithms. Nevertheless, machine learning models used in modern image recognition systems consist of millions of parameters that usually require significant…