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The broad applicability of Quadratic Unconstrained Binary Optimization (QUBO) constitutes a general-purpose modeling framework for combinatorial optimization problems and are a required format for gate array and quantum annealing computers.…
Variational quantum circuits have arisen as an important method in quantum computing. A crucial step of it is parameter optimization, which is typically tackled through gradient-descent techniques. We advantageously explore instead the use…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…
In this paper, we investigate the framework of Online Convex Optimization (OCO) for online learning. OCO offers a very powerful online learning framework for many applications. In this context, we study a specific framework of OCO called…
Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present an application level benchmarking framework for near-term quantum…
This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue…
This paper describes a new efficient conjugate subgradient algorithm which minimizes a convex function containing a least squares fidelity term and an absolute value regularization term. This method is successfully applied to the inversion…
The paper introduces the first formulation of convex Q-learning for Markov decision processes with function approximation. The algorithms and theory rest on a relaxation of a dual of Manne's celebrated linear programming characterization of…
We expose in a tutorial fashion the mechanisms which underlie the synthesis of optimization algorithms based on dynamic integral quadratic constraints. We reveal how these tools from robust control allow to design accelerated gradient…
This paper presents a formal framework and proposes algorithms to extend forecast reconciliation to discrete-valued data to extend forecast reconciliation to discrete-valued data, including low counts. A novel method is introduced based on…
This paper proposes QPALM, a proximal augmented Lagrangian method based on quadratic approximations, for solving nonlinear programming problems with weakly convex objective and constraint functions. The algorithm is constructed by…
In this paper, we propose a learning-to-optimize (L2O) framework to accelerate solving parametric mixed-integer quadratic programming (MIQP) problems, with a particular focus on mixed-integer model predictive control (MI-MPC) applications.…
In machine learning, fewer features reduce model complexity. Carefully assessing the influence of each input feature on the model quality is therefore a crucial preprocessing step. We propose a novel feature selection algorithm based on a…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…
The quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm (VQA) ideal for noisy intermediate-scale quantum (NISQ) processors, and is highly successful in solving combinatorial optimization problems (COPs). It…
Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause…
This paper describes an application of the Quantum Approximate Optimisation Algorithm (QAOA) to efficiently find approximate solutions for computational problems contained in the polynomially bounded NP optimisation complexity class (NPO…
We propose and compare Constraint Programming (CP) and Quantum Annealing (QA) approaches for rolling stock assignment optimisation considering necessary maintenance tasks. In the CP approach, we model the problem with an Alldifferent…