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Bayesian optimization is a powerful global optimization technique for expensive black-box functions. One of its shortcomings is that it requires auxiliary optimization of an acquisition function at each iteration. This auxiliary…
The Binary Polynomial Optimization (BPO) problem is defined as the problem of maximizing a given polynomial function over all binary points. The main contribution of this paper is to draw a novel connection between BPO and the field of…
The optimization of expensive-to-evaluate black-box functions over combinatorial structures is an ubiquitous task in machine learning, engineering and the natural sciences. The combinatorial explosion of the search space and costly…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…
In this paper, we consider the decentralized optimization problems with generalized orthogonality constraints, where both the objective function and the constraint exhibit a distributed structure. Such optimization problems, albeit…
Many real-world applications require solving families of expensive multi-objective optimization problems~(EMOPs) under varying operational conditions. This can be formulated as parametric expensive multi-objective optimization problems…
Bayesian optimization (BO) is a popular algorithm for solving challenging optimization tasks. It is designed for problems where the objective function is expensive to evaluate, perhaps not available in exact form, without gradient…
We address the non-convex optimisation problem of finding a sparse matrix on the Stiefel manifold (matrices with mutually orthogonal columns of unit length) that maximises (or minimises) a quadratic objective function. Optimisation problems…
We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…
Complex single-objective bounded problems are often difficult to solve. In evolutionary computation methods, since the proposal of differential evolution algorithm in 1997, it has been widely studied and developed due to its simplicity and…
We develop a general method for extending Markov processes to a larger state space such that the added points form a polar set. The so obtained extension is an improvement on the standard trivial extension in which case the process is made…
Time-varying stochastic optimization problems frequently arise in machine learning practice (e.g. gradual domain shift, object tracking, strategic classification). Although most problems are solved in discrete time, the underlying process…
The need of fast distributed solvers for optimization problems in networked systems has motivated the recent development of the Fast-Lipschitz optimization framework. In such an optimization, problems satisfying certain qualifying…
The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued functions, with an emphasis on functions satisfying a certain composite representation. This will be conducted under the parabolic regularity, a…
It has recently been shown that complete Bernstein functions of the Laplace operator map the Dirichlet boundary condition of a related elliptic PDE to the Neumann boundary condition. The importance of this mapping consists in being able to…
The rational covariance extension problem (RCEP) is an important problem in systems and control occurring in such diverse fields as control, estimation, system identification, and signal and image processing, leading to many fundamental…
Distributionally robust optimization has emerged as an attractive way to train robust machine learning models, capturing data uncertainty and distribution shifts. Recent statistical analyses have proved that generalization guarantees of…
We describe a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organized critical models of co-evolution such as the Bak-Sneppen model. The method, called Extremal Optimization,…
Bayesian optimization is a powerful optimization tool for problems where native first-order derivatives are unavailable. Recently, constrained Bayesian optimization (CBO) has been applied to many engineering applications where constraints…
We study the optimal contract problem in the \emph{combinatorial actions} framework of D\"utting et al.~[FOCS'21], where a principal delegates a project to an agent who chooses a subset of hidden, costly actions, and the resulting reward is…