Related papers: Branch and Bound Algorithms for Maximizing Expecte…
A novel efficient method for computing the Knowledge-Gradient policy for Continuous Parameters (KGCP) for deterministic optimization is derived. The differences with Expected Improvement (EI), a popular choice for Bayesian optimization of…
The expected improvement (EI) algorithm is a popular strategy for information collection in optimization under uncertainty. The algorithm is widely known to be too greedy, but nevertheless enjoys wide use due to its simplicity and ability…
This work deals with parallel optimization of expensive objective functions which are modeled as sample realizations of Gaussian processes. The study is formalized as a Bayesian optimization problem, or continuous multi-armed bandit…
We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
A computer code or simulator is a mathematical representation of a physical system, for example a set of differential equations. Running the code with given values of the vector of inputs, x, leads to an output y(x) or several such outputs.…
Branch-and-cut is the most widely used algorithm for solving integer programs, employed by commercial solvers like CPLEX and Gurobi. Branch-and-cut has a wide variety of tunable parameters that have a huge impact on the size of the search…
The ability of Gaussian processes (GPs) to predict the behavior of dynamical systems as a more sample-efficient alternative to parametric models seems promising for real-world robotics research. However, the computational complexity of GPs…
The expected improvement (EI) algorithm is one of the most popular strategies for optimization under uncertainty due to its simplicity and efficiency. Despite its popularity, the theoretical aspects of this algorithm have not been properly…
This paper deals with the construction of a metamodel (i.e. a simplified mathematical model) for a stochastic computer code (also called stochastic numerical model or stochastic simulator), where stochastic means that the code maps the…
The analysis of computer models can be aided by the construction of surrogate models, or emulators, that statistically model the numerical computer model. Increasingly, computer models are becoming stochastic, yielding different outputs…
Genetic programming (GP) is an evolutionary computation technique to solve problems in an automated, domain-independent way. Rather than identifying the optimum of a function as in more traditional evolutionary optimization, the aim of GP…
Physical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical…
In many real-world applications, we are interested in approximating black-box, costly functions as accurately as possible with the smallest number of function evaluations. A complex computer code is an example of such a function. In this…
Computer experiments have become ubiquitous in science and engineering. Commonly, runs of these simulations demand considerable time and computing, making experimental design extremely important in gaining high quality information with…
Bayesian Optimization (BO) links Gaussian Process (GP) surrogates with sequential design toward optimizing expensive-to-evaluate black-box functions. Example design heuristics, or so-called acquisition functions, like expected improvement…
Machine learning algorithms frequently require careful tuning of model hyperparameters, regularization terms, and optimization parameters. Unfortunately, this tuning is often a "black art" that requires expert experience, unwritten rules of…
Making good predictions of a physical system using a computer code requires the inputs to be carefully specified. Some of these inputs called control variables have to reproduce physical conditions whereas other inputs, called parameters,…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes…
Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…