Related papers: Bayesian Optimization with Shape Constraints

This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…

Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…

Bayesian optimization (BO) developed as an approach for the efficient optimization of expensive black-box functions without gradient information. A typical BO paper introduces a new approach and compares it to some alternatives on simulated…

Bayesian optimization (BO) is a powerful approach to sample-efficient optimization of black-box functions. However, in settings with very few function evaluations, a successful application of BO may require transferring information from…

We present first a brief review of the existing literature on shape optimization, stressing the recent use of Hamiltonian systems in topology optimization. In the second section, we collect some preliminaries on the implicit parametrization…

We consider the problem of shape restricted nonparametric regression on a closed set X ?\in R; where it is reasonable to assume the function has no more than H local extrema interior to X: Following a Bayesian approach we develop a…

Fully convolutional U-shaped neural networks have largely been the dominant approach for pixel-wise image segmentation. In this work, we tackle two defects that hinder their deployment in real-world applications: 1) Predictions lack…

Bayesian optimization has emerged at the forefront of expensive black-box optimization due to its data efficiency. Recent years have witnessed a proliferation of studies on the development of new Bayesian optimization algorithms and their…

Adjustable hyperparameters of machine learning models typically impact various key trade-offs such as accuracy, fairness, robustness, or inference cost. Our goal in this paper is to find a configuration that adheres to user-specified limits…

Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…

Bayesian optimization is a popular framework for efficiently tackling black-box search problems. As a rule, these algorithms operate by iteratively choosing what to evaluate next until some predefined budget has been exhausted. We…

The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. The support function can be used in order to approximate solutions to such problems by finite dimensional optimization…

State-of-the-art multi-objective optimization often assumes a known utility function, learns it interactively, or computes the full Pareto front-each requiring costly expert input.~Real-world problems, however, involve implicit preferences…

We apply the PAC-Bayes theory to the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-bounds) and explicit trade-off…

Bayesian Optimisation (BO) is a technique used in optimising a $D$-dimensional function which is typically expensive to evaluate. While there have been many successes for BO in low dimensions, scaling it to high dimensions has been…

Modern deep learning tools are remarkably effective in addressing intricate problems. However, their operation as black-box models introduces increased uncertainty in predictions. Additionally, they contend with various challenges,…

We consider Bayesian optimization of objective functions of the form $\rho[ F(x, W) ]$, where $F$ is a black-box expensive-to-evaluate function and $\rho$ denotes either the VaR or CVaR risk measure, computed with respect to the randomness…

In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points…

We introduce a unified framework for contextual and causal Bayesian optimisation, which aims to design intervention policies maximising the expectation of a target variable. Our approach leverages both observed contextual information and…

This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…