Preprint of paper to appear in the proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS) 2019, Naha, Okinawa, Japan. PMLR: Volume 89
Bayesian optimisation (BO) has been a successful approach to optimise functions which are expensive to evaluate and whose observations are noisy. Classical BO algorithms, however, do not account for errors about the location where observations are taken, which is a common issue in problems with physical components. In these cases, the estimation of the actual query location is also subject to uncertainty. In this context, we propose an upper confidence bound (UCB) algorithm for BO problems where both the outcome of a query and the true query location are uncertain. The algorithm employs a Gaussian process model that takes probability distributions as inputs. Theoretical results are provided for both the proposed algorithm and a conventional UCB approach within the uncertain-inputs setting. Finally, we evaluate each method's performance experimentally, comparing them to other input noise aware BO approaches on simulated scenarios involving synthetic and real data.
Many real-world optimisation problems such as hyperparameter tuning in machine learning or simulation-based optimisation can be formulated as expensive-to-evaluate black-box functions. A popular approach to tackle such problems is Bayesian optimisation (BO), which builds a response surface model based on the data collected so far, and uses the mean and uncertainty predicted by the model to decide what information to collect next. In this paper, we propose a novel variant of the well-known Knowledge Gradient acquisition function that allows it to handle constraints. We empirically compare the n…
Efficient optimisation of black-box problems that comprise both continuous and categorical inputs is important, yet poses significant challenges. We propose a new approach, Continuous and Categorical Bayesian Optimisation (CoCaBO), which combines the strengths of multi-armed bandits and Bayesian optimisation to select values for both categorical and continuous inputs. We model this mixed-type space using a Gaussian Process kernel, designed to allow sharing of information across multiple categorical variables, each with multiple possible values; this allows CoCaBO to leverage all available data…
Sparse Gaussian Processes are a key component of high-throughput Bayesian Optimisation (BO) loops; however, we show that existing methods for allocating their inducing points severely hamper optimisation performance. By exploiting the quality-diversity decomposition of Determinantal Point Processes, we propose the first inducing point allocation strategy designed specifically for use in BO. Unlike existing methods which seek only to reduce global uncertainty in the objective function, our approach provides the local high-fidelity modelling of promising regions required for precise optimisation…
Huawei R&D UK（华为英国研发部）；University of Cambridge（剑桥大学）；University College London（伦敦大学学院）
Bayesian optimisation presents a sample-efficient methodology for global optimisation. Within this framework, a crucial performance-determining subroutine is the maximisation of the acquisition function, a task complicated by the fact that acquisition functions tend to be non-convex and thus nontrivial to optimise. In this paper, we undertake a comprehensive empirical study of approaches to maximise the acquisition function. Additionally, by deriving novel, yet mathematically equivalent, compositional forms for popular acquisition functions, we recast the maximisation task as a compositional o…
Wind energy is one of the cleanest renewable electricity sources and can help in addressing the challenge of climate change. One of the drawbacks of wind-generated energy is the large space necessary to install a wind farm; this arises from the fact that placing wind turbines in a limited area would hinder their productivity and therefore not be economically convenient. This naturally leads to an optimisation problem, which has three specific challenges: (1) multiple conflicting objectives (2) computationally expensive simulation models and (3) optimisation over design sets instead of design v…
In order to improve the performance of Bayesian optimisation, we develop a modified Gaussian process upper confidence bound (GP-UCB) acquisition function. This is done by sampling the exploration-exploitation trade-off parameter from a distribution. We prove that this allows the expected trade-off parameter to be altered to better suit the problem without compromising a bound on the function's Bayesian regret. We also provide results showing that our method achieves better performance than GP-UCB in a range of real-world and synthetic problems.
Many real-world optimisation problems are defined over both categorical and continuous variables, yet efficient optimisation methods such asBayesian Optimisation (BO) are not designed tohandle such mixed-variable search spaces. Recent approaches to this problem cast the selection of the categorical variables as a bandit problem, operating independently alongside a BO component which optimises the continuous variables. In this paper, we adopt a holistic view and aim to consolidate optimisation of the categorical and continuous sub-spaces under a single acquisition metric. We derive candidates f…
University of Oxford（牛津大学）；Amazon（亚马逊）；RMIT University（皇家墨尔本理工大学）
High-dimensional black-box optimisation remains an important yet notoriously challenging problem. Despite the success of Bayesian optimisation methods on continuous domains, domains that are categorical, or that mix continuous and categorical variables, remain challenging. We propose a novel solution -- we combine local optimisation with a tailored kernel design, effectively handling high-dimensional categorical and mixed search spaces, whilst retaining sample efficiency. We further derive convergence guarantee for the proposed approach. Finally, we demonstrate empirically that our method outp…
Motivated by the success of Bayesian optimisation algorithms in the Euclidean space, we propose a novel approach to construct Intrinsic Bayesian optimisation (In-BO) on manifolds with a primary focus on complex constrained domains or irregular-shaped spaces arising as submanifolds of R2, R3 and beyond. Data may be collected in a spatial domain but restricted to a complex or intricately structured region corresponding to a geographic feature, such as lakes. Traditional Bayesian Optimisation (Tra-BO) defined with a Radial basis function (RBF) kernel cannot accommodate these complex constrained c…
Bayesian optimisation (BO) uses probabilistic surrogate models - usually Gaussian processes (GPs) - for the optimisation of expensive black-box functions. At each BO iteration, the GP hyperparameters are fit to previously-evaluated data by maximising the marginal likelihood. However, this fails to account for uncertainty in the hyperparameters themselves, leading to overconfident model predictions. This uncertainty can be accounted for by taking the Bayesian approach of marginalising out the model hyperparameters. We investigate whether a fully-Bayesian treatment of the Gaussian process hyperp…
Information-theoretic Bayesian optimisation techniques have demonstrated state-of-the-art performance in tackling important global optimisation problems. However, current information-theoretic approaches require many approximations in implementation, introduce often-prohibitive computational overhead and limit the choice of kernels available to model the objective. We develop a fast information-theoretic Bayesian Optimisation method, FITBO, that avoids the need for sampling the global minimiser, thus significantly reducing computational overhead. Moreover, in comparison with existing approache…
Deakin University（迪肯大学）；Centre for Pattern Recognition and Data Analytics（模式识别与数据分析中心）；Institute for Frontier Materials（前沿材料研究所）
Real world experiments are expensive, and thus it is important to reach a target in minimum number of experiments. Experimental processes often involve control variables that changes over time. Such problems can be formulated as a functional optimisation problem. We develop a novel Bayesian optimisation framework for such functional optimisation of expensive black-box processes. We represent the control function using Bernstein polynomial basis and optimise in the coefficient space. We derive the theory and practice required to dynamically adjust the order of the polynomial degree, and show ho…
Bayesian optimisation is a well-known sample-efficient method for the optimisation of expensive black-box functions. However when dealing with big search spaces the algorithm goes through several low function value regions before reaching the optimum of the function. Since the function evaluations are expensive in terms of both money and time, it may be desirable to alleviate this problem. One approach to subside this cold start phase is to use prior knowledge that can accelerate the optimisation. In its standard form, Bayesian optimisation assumes the likelihood of any point in the search spa…
While sample efficiency is the main motive for use of Bayesian optimisation when black-box functions are expensive to evaluate, the standard approach based on type II maximum likelihood (ML-II) may fail and result in disappointing performance in small-sample trials. The paper provides three compelling reasons to adopt fully Bayesian optimisation (FBO) as an alternative. First, failures of ML-II are more commonplace than implied by the existing studies using the contrived settings. Second, FBO is more robust than ML-II, and the price of robustness is almost trivial. Third, FBO has become simple…
Bayesian optimisation is a sample-efficient search methodology that holds great promise for accelerating drug and materials discovery programs. A frequently-overlooked modelling consideration in Bayesian optimisation strategies however, is the representation of heteroscedastic aleatoric uncertainty. In many practical applications it is desirable to identify inputs with low aleatoric noise, an example of which might be a material composition which consistently displays robust properties in response to a noisy fabrication process. In this paper, we propose a heteroscedastic Bayesian optimisation…
The notion of expense in Bayesian optimisation generally refers to the uniformly expensive cost of function evaluations over the whole search space. However, in some scenarios, the cost of evaluation for black-box objective functions is non-uniform since different inputs from search space may incur different costs for function evaluations. We introduce a cost-aware multi-objective Bayesian optimisation with non-uniform evaluation cost over objective functions by defining cost-aware constraints over the search space. The cost-aware constraints are a sorted tuple of indexes that demonstrate the …
Bayesian optimisation is a powerful tool to solve expensive black-box problems, but fails when the stationary assumption made on the objective function is strongly violated, which is the case in particular for ill-conditioned or discontinuous objectives. We tackle this problem by proposing a new Bayesian optimisation framework that only considers the ordering of variables, both in the input and output spaces, to fit a Gaussian process in a latent space. By doing so, our approach is agnostic to the original metrics on the original spaces. We propose two algorithms, respectively based on an opti…
We introduce a novel framework for the estimation of the posterior distribution over the weights of a neural network, based on a new probabilistic interpretation of adaptive optimisation algorithms such as AdaGrad and Adam. We demonstrate the effectiveness of our Bayesian Adam method, Badam, by experimentally showing that the learnt uncertainties correctly relate to the weights' predictive capabilities by weight pruning. We also demonstrate the quality of the derived uncertainty measures by comparing the performance of Badam to standard methods in a Thompson sampling setting for multi-armed ba…
University of Oxford（牛津大学）；Mind Foundry Ltd.（Mind Foundry有限公司）；Oxford-Man Institute of Quantitative Finance（牛津-曼定量金融研究所）
Batch Bayesian optimisation (BO) has been successfully applied to hyperparameter tuning using parallel computing, but it is wasteful of resources: workers that complete jobs ahead of others are left idle. We address this problem by developing an approach, Penalising Locally for Asynchronous Bayesian Optimisation on $k$ workers (PLAyBOOK), for asynchronous parallel BO. We demonstrate empirically the efficacy of PLAyBOOK and its variants on synthetic tasks and a real-world problem. We undertake a comparison between synchronous and asynchronous BO, and show that asynchronous BO often outperforms …
School of Computer Science, the University of Sydney（悉尼大学计算机学院）；Australian Research Council Centre for Data Analytics for Resources and Environments (DARE)（澳大利亚研究理事会资源与环境数据分析中心（DARE））；NVIDIA（英伟达）
Model predictive control (MPC) has been successful in applications involving the control of complex physical systems. This class of controllers leverages the information provided by an approximate model of the system's dynamics to simulate the effect of control actions. MPC methods also present a few hyper-parameters which may require a relatively expensive tuning process by demanding interactions with the physical system. Therefore, we investigate fine-tuning MPC methods in the context of stochastic MPC, which presents extra challenges due to the randomness of the controller's actions. In the…
School of Computer Science and Statistics, Trinity College Dublin（都柏林圣三一学院计算机科学与统计学学院）；Dalle Molle Institute for Artificial Intelligence Research (IDSIA)（达勒·莫勒人工智能研究所（IDSIA））
In this work we introduce a new framework for multi-objective Bayesian optimisation where the multi-objective functions can only be accessed via choice judgements, such as ``I pick options A,B,C among this set of five options A,B,C,D,E''. The fact that the option D is rejected means that there is at least one option among the selected ones A,B,C that I strictly prefer over D (but I do not have to specify which one). We assume that there is a latent vector function f for some dimension $n_e$ which embeds the options into the real vector space of dimension n, so that the choice set can be repres…
Bayesian optimisation (BO) is widely used to optimise stochastic black box functions. While most BO approaches focus on optimising conditional expectations, many applications require risk-averse strategies and alternative criteria accounting for the distribution tails need to be considered. In this paper, we propose new variational models for Bayesian quantile and expectile regression that are well-suited for heteroscedastic noise settings. Our models consist of two latent Gaussian processes accounting respectively for the conditional quantile (or expectile) and the scale parameter of an asymm…
Center for Pattern Recognition and Data Analytics (PRaDA)（模式识别与数据分析中心（PRaDA））；Deakin University（迪肯大学）
In this paper we consider the problem of finding stable maxima of expensive (to evaluate) functions. We are motivated by the optimisation of physical and industrial processes where, for some input ranges, small and unavoidable variations in inputs lead to unacceptably large variation in outputs. Our approach uses multiple gradient Gaussian Process models to estimate the probability that worst-case output variation for specified input perturbation exceeded the desired maxima, and these probabilities are then used to (a) guide the optimisation process toward solutions satisfying our stability cr…
Simulators often require calibration inputs estimated from real world data and the quality of the estimate can significantly affect simulation output. Particularly when performing simulation optimisation to find an optimal solution, the uncertainty in the inputs significantly affects the quality of the found solution. One remedy is to search for the solution that has the best performance on average over the uncertain range of inputs yielding an optimal compromise solution. We consider the more general setting where a user may choose between either running simulations or instead collecting real…
Return of the Latent Space COWBOYS: Re-thinking the use of VAEs for Bayesian Optimisation of Structured Spaces
School of Mathematical Sciences, Lancaster University, UK（数学科学学院，兰卡斯特大学）；Department of Applied Maths and Theoretical Physics, University of Cambridge, UK（应用数学与理论物理系，剑桥大学）
This paper describes a general-purpose extension of max-value entropy search, a popular approach for Bayesian Optimisation (BO). A novel approximation is proposed for the information gain -- an information-theoretic quantity central to solving a range of BO problems, including noisy, multi-fidelity and batch optimisations across both continuous and highly-structured discrete spaces. Previously, these problems have been tackled separately within information-theoretic BO, each requiring a different sophisticated approximation scheme, except for batch BO, for which no computationally-lightweight …
Imperial College London（伦敦帝国理工学院）；University of Manchester（曼彻斯特大学）；University of Edinburgh（爱丁堡大学）；Alan Turing Institute（艾伦·图灵研究所）
Bayesian Optimisation (BO) methods seek to find global optima of objective functions which are only available as a black-box or are expensive to evaluate. Such methods construct a surrogate model for the objective function, quantifying the uncertainty in that surrogate through Bayesian inference. Objective evaluations are sequentially determined by maximising an acquisition function at each step. However, this ancilliary optimisation problem can be highly non-trivial to solve, due to the non-convexity of the acquisition function, particularly in the case of batch Bayesian optimisation, where m…
Bayesian optimisation (BO) algorithms have shown remarkable success in applications involving expensive black-box functions. Traditionally BO has been set as a sequential decision-making process which estimates the utility of query points via an acquisition function and a prior over functions, such as a Gaussian process. Recently, however, a reformulation of BO via density-ratio estimation (BORE) allowed reinterpreting the acquisition function as a probabilistic binary classifier, removing the need for an explicit prior over functions and increasing scalability. In this paper, we present a the…
TNO（荷兰国家应用科学研究院）；University of Exeter（埃克塞特大学）；Swansea University（斯旺西大学）；Delft University of Technology（代尔夫特理工大学）
Performing multi-objective Bayesian optimisation by scalarising the objectives avoids the computation of expensive multi-dimensional integral-based acquisition functions, instead of allowing one-dimensional standard acquisition functions\textemdash such as Expected Improvement\textemdash to be applied. Here, two infill criteria based on hypervolume improvement\textemdash one recently introduced and one novel\textemdash are compared with the multi-surrogate Expected Hypervolume Improvement. The reasons for the disparities in these methods' effectiveness in maximising the hypervolume of the acqu…
Bayesian Optimisation (BO) refers to a suite of techniques for global optimisation of expensive black box functions, which use introspective Bayesian models of the function to efficiently search for the optimum. While BO has been applied successfully in many applications, modern optimisation tasks usher in new challenges where conventional methods fail spectacularly. In this work, we present Dragonfly, an open source Python library for scalable and robust BO. Dragonfly incorporates multiple recently developed methods that allow BO to be applied in challenging real world settings; these include…
Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；University College London（伦敦大学学院）
Optimising the quality-of-results (QoR) of circuits during logic synthesis is a formidable challenge necessitating the exploration of exponentially sized search spaces. While expert-designed operations aid in uncovering effective sequences, the increase in complexity of logic circuits favours automated procedures. Inspired by the successes of machine learning, researchers adapted deep learning and reinforcement learning to logic synthesis applications. However successful, those techniques suffer from high sample complexities preventing widespread adoption. To enable efficient and scalable solu…
Ericsson Research（爱立信研究院）；KTH Royal Institute of Technology（KTH皇家理工学院）
Cell-free multi-user multiple input multiple output networks are a promising alternative to classical cellular architectures, since they have the potential to provide uniform service quality and high resource utilisation over the entire coverage area of the network. To realise this potential, previous works have developed radio resource management mechanisms using various optimisation engines. In this work, we consider the problem of overall ergodic spectral efficiency maximisation in the context of uplink-downlink data power control in cell-free networks. To solve this problem in large networ…
Secondmind（Secondmind公司）；University of Cambridge（剑桥大学）
Sparse Gaussian Processes are a key component of high-throughput Bayesian optimisation (BO) loops -- an increasingly common setting where evaluation budgets are large and highly parallelised. By using representative subsets of the available data to build approximate posteriors, sparse models dramatically reduce the computational costs of surrogate modelling by relying on a small set of pseudo-observations, the so-called inducing points, in lieu of the full data set. However, current approaches to design inducing points are not appropriate within BO loops as they seek to reduce global uncertain…
Batch Bayesian optimisation (BO) is a successful technique for the optimisation of expensive black-box functions. Asynchronous BO can reduce wallclock time by starting a new evaluation as soon as another finishes, thus maximising resource utilisation. To maximise resource allocation, we develop a novel asynchronous BO method, AEGiS (Asynchronous $ε$-Greedy Global Search) that combines greedy search, exploiting the surrogate's mean prediction, with Thompson sampling and random selection from the approximate Pareto set describing the trade-off between exploitation (surrogate mean prediction) and…
We present a multi-objective Bayesian optimisation algorithm that allows the user to express preference-order constraints on the objectives of the type "objective A is more important than objective B". These preferences are defined based on the stability of the obtained solutions with respect to preferred objective functions. Rather than attempting to find a representative subset of the complete Pareto front, our algorithm selects those Pareto-optimal points that satisfy these constraints. We formulate a new acquisition function based on expected improvement in dominated hypervolume (EHI) to e…
Bayesian optimisation is a popular approach for optimising expensive black-box functions. The next location to be evaluated is selected via maximising an acquisition function that balances exploitation and exploration. Gaussian processes, the surrogate models of choice in Bayesian optimisation, are often used with a constant prior mean function equal to the arithmetic mean of the observed function values. We show that the rate of convergence can depend sensitively on the choice of mean function. We empirically investigate 8 mean functions (constant functions equal to the arithmetic mean, minim…
Heuristics in theorem provers are often parameterised. Modern theorem provers such as Vampire utilise a wide array of heuristics to control the search space explosion, thereby requiring optimisation of a large set of parameters. An exhaustive search in this multi-dimensional parameter space is intractable in most cases, yet the performance of the provers is highly dependent on the parameter assignment. In this work, we introduce a principled probablistic framework for heuristics optimisation in theorem provers. We present results using a heuristic for premise selection and The Archive of Forma…
Current neural architecture search (NAS) strategies focus only on finding a single, good, architecture. They offer little insight into why a specific network is performing well, or how we should modify the architecture if we want further improvements. We propose a Bayesian optimisation (BO) approach for NAS that combines the Weisfeiler-Lehman graph kernel with a Gaussian process surrogate. Our method optimises the architecture in a highly data-efficient manner: it is capable of capturing the topological structures of the architectures and is scalable to large graphs, thus making the high-dimen…
The University of Sydney（悉尼大学）；University of Sao Paulo（圣保罗大学）
In the automation of many kinds of processes, the observable outcome can often be described as the combined effect of an entire sequence of actions, or controls, applied throughout its execution. In these cases, strategies to optimise control policies for individual stages of the process might not be applicable, and instead the whole policy might have to be optimised at once. On the other hand, the cost to evaluate the policy's performance might also be high, being desirable that a solution can be found with as few interactions as possible with the real system. We consider the problem of optim…
Quality Diversity (QD) algorithms such as MAP-Elites are a class of optimisation techniques that attempt to find a set of high-performing points from an objective function while enforcing behavioural diversity of the points over one or more interpretable, user chosen, feature functions. In this paper we propose the Bayesian Optimisation of Elites (BOP-Elites) algorithm that uses techniques from Bayesian Optimisation to explicitly model both quality and diversity with Gaussian Processes. By considering user defined regions of the feature space as 'niches' our task is to find the optimal solutio…
Bayesian Optimisation (BO) refers to a class of methods for global optimisation of a function $f$ which is only accessible via point evaluations. It is typically used in settings where $f$ is expensive to evaluate. A common use case for BO in machine learning is model selection, where it is not possible to analytically model the generalisation performance of a statistical model, and we resort to noisy and expensive training and validation procedures to choose the best model. Conventional BO methods have focused on Euclidean and categorical domains, which, in the context of model selection, onl…
University of Exeter（埃克塞特大学）；Swansea University（斯旺西大学）
Optimisation problems often have multiple conflicting objectives that can be computationally and/or financially expensive. Mono-surrogate Bayesian optimisation (BO) is a popular model-based approach for optimising such black-box functions. It combines objective values via scalarisation and builds a Gaussian process (GP) surrogate of the scalarised values. The location which maximises a cheap-to-query acquisition function is chosen as the next location to expensively evaluate. While BO is an effective strategy, the use of GPs is limiting. Their performance decreases as the problem input dimensi…
Many machine learning models require a training procedure based on running stochastic gradient descent. A key element for the efficiency of those algorithms is the choice of the learning rate schedule. While finding good learning rates schedules using Bayesian optimisation has been tackled by several authors, adapting it dynamically in a data-driven way is an open question. This is of high practical importance to users that need to train a single, expensive model. To tackle this problem, we introduce an original probabilistic model for traces of optimisers, based on latent Gaussian processes a…
