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We consider the problem of optimizing a grey-box objective function, i.e., nested function composed of both black-box and white-box functions. A general formulation for such grey-box problems is given, which covers the existing grey-box…

Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More…

In this paper, we consider the problem of sequentially optimizing a black-box function $f$ based on noisy samples and bandit feedback. We assume that $f$ is smooth in the sense of having a bounded norm in some reproducing kernel Hilbert…

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…

We present two algorithms for Bayesian optimization in the batch feedback setting, based on Gaussian process upper confidence bound and Thompson sampling approaches, along with frequentist regret guarantees and numerical results.

Existing Bayesian Optimization (BO) methods typically balance exploration and exploitation to optimize costly objective functions. However, these methods often suffer from a significant one-step bias, which may lead to convergence towards…

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…

We consider online optimization with binary decision variables and convex loss functions. We design a new algorithm, binary online gradient descent (bOGD) and bound its expected dynamic regret. We provide a regret bound that holds for any…

A long-standing belief holds that Bayesian Optimization (BO) with standard Gaussian processes (GP) -- referred to as standard BO -- underperforms in high-dimensional optimization problems. While this belief seems plausible, it lacks both…

Bayesian optimization (BO) methods are useful for optimizing functions that are expensive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the…

This paper investigates the problem of efficient constrained global optimization of hybrid models that are a composition of a known white-box function and an expensive multi-output black-box function subject to noisy observations, which…

We study the sequential general online regression, known also as the sequential probability assignments, under logarithmic loss when compared against a broad class of experts. We focus on obtaining tight, often matching, lower and upper…

This paper deals with the identification of linear stochastic dynamical systems, where the unknowns include system coefficients and noise variances. Conventional approaches that rely on the maximum likelihood estimation (MLE) require…

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…

Bayesian optimization has recently attracted the attention of the automatic machine learning community for its excellent results in hyperparameter tuning. BO is characterized by the sample efficiency with which it can optimize expensive…

Most research in Bayesian optimization (BO) has focused on \emph{direct feedback} scenarios, where one has access to exact values of some expensive-to-evaluate objective. This direction has been mainly driven by the use of BO in machine…

Gaussian processes (GP) are one of the most successful frameworks to model uncertainty. However, GP optimization (e.g., GP-UCB) suffers from major scalability issues. Experimental time grows linearly with the number of evaluations, unless…

Local Bayesian optimization is a promising practical approach to solve the high dimensional black-box function optimization problem. Among them is the approximated gradient class of methods, which implements a strategy similar to gradient…

We investigate bandit convex optimization (BCO) with delayed feedback, where only the loss value of the action is revealed under an arbitrary delay. Let $n,T,\bar{d}$ denote the dimensionality, time horizon, and average delay, respectively.…

Scaling Bayesian optimisation (BO) to high-dimensional search spaces is a active and open research problems particularly when no assumptions are made on function structure. The main reason is that at each iteration, BO requires to find…