相关论文: A Lipschitz Exploration-Exploitation Scheme for Ba…

Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic…

In the paper, the global optimization problem of a multidimensional "black-box" function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. A new efficient algorithm for solving this…

This paper deals with two kinds of the one-dimensional global optimization problems over a closed finite interval: (i) the objective function $f(x)$ satisfies the Lipschitz condition with a constant $L$; (ii) the first derivative of $f(x)$…

In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy…

Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…

Bayesian Optimization (BO) is a widely-used method for optimizing expensive-to-evaluate black-box functions. Traditional BO assumes that the learner has full control over all query variables without additional constraints. However, in many…

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…

The aim of black-box optimization is to optimize an objective function within the constraints of a given evaluation budget. In this problem, it is generally assumed that the computational cost for evaluating a point is large; thus, it is…

An exciting branch of machine learning research focuses on methods for learning, optimizing, and integrating unknown functions that are difficult or costly to evaluate. A popular Bayesian approach to this problem uses a Gaussian process…

Many expensive black-box optimisation problems are sensitive to their inputs. In these problems it makes more sense to locate a region of good designs, than a single-possibly fragile-optimal design. Expensive black-box functions can be…

Bayesian optimization has recently emerged as a popular and efficient tool for global optimization and hyperparameter tuning. Currently, the established Bayesian optimization practice requires a user-defined bounding box which is assumed to…

Recently, there has been rising interest in Bayesian optimization -- the optimization of an unknown function with assumptions usually expressed by a Gaussian Process (GP) prior. We study an optimization strategy that directly uses an…

Sequential decision tasks with incomplete information are characterized by the exploration problem; namely the trade-off between further exploration for learning more about the environment and immediate exploitation of the accrued…

This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted…

Bayesian optimization (BO) and its batch extensions are successful for optimizing expensive black-box functions. However, these traditional BO approaches are not yet ideal for optimizing less expensive functions when the computational cost…

We consider Bayesian optimization using Gaussian Process models, also referred to as kernel-based bandit optimization. We study the methodology of exploring the domain using random samples drawn from a distribution. We show that this random…

Bayesian optimization (BO) has emerged during the last few years as an effective approach to optimizing black-box functions where direct queries of the objective are expensive. In this paper we consider the case where direct access to the…

Reinforcement learning systems are often concerned with balancing exploration of untested actions against exploitation of actions that are known to be good. The benefit of exploration can be estimated using the classical notion of Value of…

We study the problem of estimating the average of a Lipschitz continuous function $f$ defined over a metric space, by querying $f$ at only a single point. More specifically, we explore the role of randomness in drawing this sample. Our goal…

Bayesian optimisation is a popular method for efficient optimisation of expensive black-box functions. Traditionally, BO assumes that the search space is known. However, in many problems, this assumption does not hold. To this end, we…