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 dimensionality increases, and their computational complexity scales cubically with the amount of data. To address these limitations, we extend previous work on BO by density-ratio estimation (BORE) to the multi-objective setting. BORE links the computation of the probability of improvement acquisition function to that of probabilistic classification. This enables the use of state-of-the-art classifiers in a BO-like framework. In this work we present MBORE: multi-objective Bayesian optimisation by density-ratio estimation, and compare it to BO across a range of synthetic and real-world benchmarks. We find that MBORE performs as well as or better than BO on a wide variety of problems, and that it outperforms BO on high-dimensional and real-world problems.
The optimization and machine learning toolkit (OMLT) is an open-source software package incorporating neural network and gradient-boosted tree surrogate models, which have been trained using machine learning, into larger optimization problems. We discuss the advances in optimization technology that made OMLT possible and show how OMLT seamlessly integrates with the algebraic modeling language Pyomo. We demonstrate how to use OMLT for solving decision-making problems in both computer science and engineering.
Antibodies are canonically Y-shaped multimeric proteins capable of highly specific molecular recognition. The CDRH3 region located at the tip of variable chains of an antibody dominates antigen-binding specificity. Therefore, it is a priority to design optimal antigen-specific CDRH3 regions to develop therapeutic antibodies. However, the combinatorial nature of CDRH3 sequence space makes it impossible to search for an optimal binding sequence exhaustively and efficiently using computational approaches. Here, we present \texttt{AntBO}: a combinatorial Bayesian optimisation framework enabling efficient \textit{in silico} design of the CDRH3 region. Ideally, antibodies are expected to have high target specificity and developability. We introduce a CDRH3 trust region that restricts the search to sequences with favourable developability scores to achieve this goal. For benchmarking, \texttt{AntBO} uses the \texttt{Absolut!} software suite as a black-box oracle to score the target specificity and affinity of designed antibodies \textit{in silico} in an unconstrained fashion~\citep{robert2021one}. The experiments performed for $159$ discretised antigens used in \texttt{Absolut!} demonstrate the benefit of \texttt{AntBO} in designing CDRH3 regions with diverse biophysical properties. In under $200$ calls to black-box oracle, \texttt{AntBO} can suggest antibody sequences that outperform the best binding sequence drawn from 6.9 million experimentally obtained CDRH3s and a commonly used genetic algorithm baseline. Additionally, \texttt{AntBO} finds very-high affinity CDRH3 sequences in only 38 protein designs whilst requiring no domain knowledge. We conclude \texttt{AntBO} brings automated antibody design methods closer to what is practically viable for in vitro experimentation.
In recent years, a significant amount of research efforts concentrated on adversarial attacks on images, while adversarial video attacks have seldom been explored. We propose an adversarial attack strategy on videos, called DeepSAVA. Our model includes both additive perturbation and spatial transformation by a unified optimisation framework, where the structural similarity index (SSIM) measure is adopted to measure the adversarial distance. We design an effective and novel optimisation scheme which alternatively utilizes Bayesian optimisation to identify the most influential frame in a video and Stochastic gradient descent (SGD) based optimisation to produce both additive and spatial-transformed perturbations. Doing so enables DeepSAVA to perform a very sparse attack on videos for maintaining human imperceptibility while still achieving state-of-the-art performance in terms of both attack success rate and adversarial transferability. Our intensive experiments on various types of deep neural networks and video datasets confirm the superiority of DeepSAVA.
Graph neural networks, a popular class of models effective in a wide range of graph-based learning tasks, have been shown to be vulnerable to adversarial attacks. While the majority of the literature focuses on such vulnerability in node-level classification tasks, little effort has been dedicated to analysing adversarial attacks on graph-level classification, an important problem with numerous real-life applications such as biochemistry and social network analysis. The few existing methods often require unrealistic setups, such as access to internal information of the victim models, or an impractically-large number of queries. We present a novel Bayesian optimisation-based attack method for graph classification models. Our method is black-box, query-efficient and parsimonious with respect to the perturbation applied. We empirically validate the effectiveness and flexibility of the proposed method on a wide range of graph classification tasks involving varying graph properties, constraints and modes of attack. Finally, we analyse common interpretable patterns behind the adversarial samples produced, which may shed further light on the adversarial robustness of graph classification models.
Bayesian optimization (BO) is an approach to globally optimizing black-box objective functions that are expensive to evaluate. BO-powered experimental design has found wide application in materials science, chemistry, experimental physics, drug development, etc. This work aims to bring attention to the benefits of applying BO in designing experiments and to provide a BO manual, covering both methodology and software, for the convenience of anyone who wants to apply or learn BO. In particular, we briefly explain the BO technique, review all the applications of BO in additive manufacturing, compare and exemplify the features of different open BO libraries, unlock new potential applications of BO to other types of data (e.g., preferential output). This article is aimed at readers with some understanding of Bayesian methods, but not necessarily with knowledge of additive manufacturing; the software performance overview and implementation instructions are instrumental for any experimental-design practitioner. Moreover, our review in the field of additive manufacturing highlights the current knowledge and technological trends of BO. This article has a supplementary material online.
A core goal of functional neuroimaging is to study how the environment is processed in the brain. The mainstream paradigm involves concurrently measuring a broad spectrum of brain responses to a small set of environmental features preselected with reference to previous studies or a theoretical framework. As a complement, we invert this approach by allowing the investigator to record the modulation of a preselected brain response by a broad spectrum of environmental features. Our approach is optimal when theoretical frameworks or previous empirical data are impoverished. By using a prespecified closed-loop design, the approach addresses fundamental challenges of reproducibility and generalisability in brain research. These conditions are particularly acute when studying the developing brain, where our theories based on adult brain function may fundamentally misrepresent the topography of infant cognition and where there are substantial practical challenges to data acquisition. Our methodology employs machine learning to map modulation of a neural feature across a space of experimental stimuli. Our method collects, processes and analyses EEG brain data in real-time; and uses a neuro-adaptive Bayesian optimisation algorithm to adjust the stimulus presented depending on the prior samples of a given participant. Unsampled stimuli can be interpolated by fitting a Gaussian process regression along the dataset. We show that our method can automatically identify the face of the infant's mother through online recording of their Nc brain response to a face continuum. We can retrieve model statistics of individualised responses for each participant, opening the door for early identification of atypical development. This approach has substantial potential in infancy research and beyond for improving power and generalisability of mapping the individual cognitive topography of brain function.
Surrogate algorithms such as Bayesian optimisation are especially designed for black-box optimisation problems with expensive objectives, such as hyperparameter tuning or simulation-based optimisation. In the literature, these algorithms are usually evaluated with synthetic benchmarks which are well established but have no expensive objective, and only on one or two real-life applications which vary wildly between papers. There is a clear lack of standardisation when it comes to benchmarking surrogate algorithms on real-life, expensive, black-box objective functions. This makes it very difficult to draw conclusions on the effect of algorithmic contributions and to give substantial advice on which method to use when. A new benchmark library, EXPObench, provides first steps towards such a standardisation. The library is used to provide an extensive comparison of six different surrogate algorithms on four expensive optimisation problems from different real-life applications. This has led to new insights regarding the relative importance of exploration, the evaluation time of the objective, and the used model. We also provide rules of thumb for which surrogate algorithm to use in which situation. A further contribution is that we make the algorithms and benchmark problem instances publicly available, contributing to more uniform analysis of surrogate algorithms. Most importantly, we include the performance of the six algorithms on all evaluated problem instances. This results in a unique new dataset that lowers the bar for researching new methods as the number of expensive evaluations required for comparison is significantly reduced.
We introduce a method combining variational autoencoders (VAEs) and deep metric learning to perform Bayesian optimisation (BO) over high-dimensional and structured input spaces. By adapting ideas from deep metric learning, we use label guidance from the blackbox function to structure the VAE latent space, facilitating the Gaussian process fit and yielding improved BO performance. Importantly for BO problem settings, our method operates in semi-supervised regimes where only few labelled data points are available. We run experiments on three real-world tasks, achieving state-of-the-art results on the penalised logP molecule generation benchmark using just 3% of the labelled data required by previous approaches. As a theoretical contribution, we present a proof of vanishing regret for VAE BO.
In the field of machine learning (ML) for materials optimization, active learning algorithms, such as Bayesian Optimization (BO), have been leveraged for guiding autonomous and high-throughput experimentation systems. However, very few studies have evaluated the efficiency of BO as a general optimization algorithm across a broad range of experimental materials science domains. In this work, we evaluate the performance of BO algorithms with a collection of surrogate model and acquisition function pairs across five diverse experimental materials systems, namely carbon nanotube polymer blends, silver nanoparticles, lead-halide perovskites, as well as additively manufactured polymer structures and shapes. By defining acceleration and enhancement metrics for general materials optimization objectives, we find that for surrogate model selection, Gaussian Process (GP) with anisotropic kernels (automatic relevance detection, ARD) and Random Forests (RF) have comparable performance and both outperform the commonly used GP without ARD. We discuss the implicit distributional assumptions of RF and GP, and the benefits of using GP with anisotropic kernels in detail. We provide practical insights for experimentalists on surrogate model selection of BO during materials optimization campaigns.
The learning rate (LR) schedule is one of the most important hyper-parameters needing careful tuning in training DNNs. However, it is also one of the least automated parts of machine learning systems and usually costs significant manual effort and computing. Though there are pre-defined LR schedules and optimizers with adaptive LR, they introduce new hyperparameters that need to be tuned separately for different tasks/datasets. In this paper, we consider the question: Can we automatically tune the LR over the course of training without human involvement? We propose an efficient method, AutoLRS, which automatically optimizes the LR for each training stage by modeling training dynamics. AutoLRS aims to find an LR applied to every $\tau$ steps that minimizes the resulted validation loss. We solve this black-box optimization on the fly by Bayesian optimization (BO). However, collecting training instances for BO requires a system to evaluate each LR queried by BO's acquisition function for $\tau$ steps, which is prohibitively expensive in practice. Instead, we apply each candidate LR for only $\tau'\ll\tau$ steps and train an exponential model to predict the validation loss after $\tau$ steps. This mutual-training process between BO and the loss-prediction model allows us to limit the training steps invested in the BO search. We demonstrate the advantages and the generality of AutoLRS through extensive experiments of training DNNs for tasks from diverse domains using different optimizers. The LR schedules auto-generated by AutoLRS lead to a speedup of $1.22\times$, $1.43\times$, and $1.5\times$ when training ResNet-50, Transformer, and BERT, respectively, compared to the LR schedules in their original papers, and an average speedup of $1.31\times$ over state-of-the-art heavily-tuned LR schedules.
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 hyperparameters in BO (FBBO) leads to improved optimisation performance. Since an analytic approach is intractable, we compare FBBO using three approximate inference schemes to the maximum likelihood approach, using the Expected Improvement (EI) and Upper Confidence Bound (UCB) acquisition functions paired with ARD and isotropic Matern kernels, across 15 well-known benchmark problems for 4 observational noise settings. FBBO using EI with an ARD kernel leads to the best performance in the noise-free setting, with much less difference between combinations of BO components when the noise is increased. FBBO leads to over-exploration with UCB, but is not detrimental with EI. Therefore, we recommend that FBBO using EI with an ARD kernel as the default choice for BO.
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 outperforms the current baselines on a variety of synthetic and real-world tasks in terms of performance, computational costs, or both.
In this work we rigorously analyse assumptions inherent to black-box optimisation hyper-parameter tuning tasks. Our results on the Bayesmark benchmark indicate that heteroscedasticity and non-stationarity pose significant challenges for black-box optimisers. Based on these findings, we propose a Heteroscedastic and Evolutionary Bayesian Optimisation solver (HEBO). HEBO performs non-linear input and output warping, admits exact marginal log-likelihood optimisation and is robust to the values of learned parameters. We demonstrate HEBO's empirical efficacy on the NeurIPS 2020 Black-Box Optimisation challenge, where HEBO placed first. Upon further analysis, we observe that HEBO significantly outperforms existing black-box optimisers on 108 machine learning hyperparameter tuning tasks comprising the Bayesmark benchmark. Our findings indicate that the majority of hyper-parameter tuning tasks exhibit heteroscedasticity and non-stationarity, multi-objective acquisition ensembles with Pareto front solutions improve queried configurations, and robust acquisition maximisers afford empirical advantages relative to their non-robust counterparts. We hope these findings may serve as guiding principles for practitioners of Bayesian optimisation. All code is made available at https://github.com/huawei-noah/HEBO.
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 $\epsilon$-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 exploration (surrogate posterior variance). We demonstrate empirically the efficacy of AEGiS on synthetic benchmark problems, meta-surrogate hyperparameter tuning problems and real-world problems, showing that AEGiS generally outperforms existing methods for asynchronous BO. When a single worker is available performance is no worse than BO using expected improvement.
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.
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, minimum, median and maximum of the observed function evaluations, linear, quadratic polynomials, random forests and RBF networks), using 10 synthetic test problems and two real-world problems, and using the Expected Improvement and Upper Confidence Bound acquisition functions. We find that for design dimensions $\ge5$ using a constant mean function equal to the worst observed quality value is consistently the best choice on the synthetic problems considered. We argue that this worst-observed-quality function promotes exploitation leading to more rapid convergence. However, for the real-world tasks the more complex mean functions capable of modelling the fitness landscape may be effective, although there is no clearly optimum choice.
Neural Architecture Search (NAS) was first proposed to achieve state-of-the-art performance through the discovery of new architecture patterns, without human intervention. An over-reliance on expert knowledge in the search space design has however led to increased performance (local optima) without significant architectural breakthroughs, thus preventing truly novel solutions from being reached. In this work we 1) are the first to investigate casting NAS as a problem of finding the optimal network generator and 2) we propose a new, hierarchical and graph-based search space capable of representing an extremely large variety of network types, yet only requiring few continuous hyper-parameters. This greatly reduces the dimensionality of the problem, enabling the effective use of Bayesian Optimisation as a search strategy. At the same time, we expand the range of valid architectures, motivating a multi-objective learning approach. We demonstrate the effectiveness of this strategy on six benchmark datasets and show that our search space generates extremely lightweight yet highly competitive models.
Bayesian optimisation is a popular, surrogate model-based approach for optimising expensive black-box functions. Given a surrogate model, the next location to expensively evaluate is chosen via maximisation of a cheap-to-query acquisition function. We present an $\epsilon$-greedy procedure for Bayesian optimisation in batch settings in which the black-box function can be evaluated multiple times in parallel. Our $\epsilon$-shotgun algorithm leverages the model's prediction, uncertainty, and the approximated rate of change of the landscape to determine the spread of batch solutions to be distributed around a putative location. The initial target location is selected either in an exploitative fashion on the mean prediction, or -- with probability $\epsilon$ -- from elsewhere in the design space. This results in locations that are more densely sampled in regions where the function is changing rapidly and in locations predicted to be good (i.e close to predicted optima), with more scattered samples in regions where the function is flatter and/or of poorer quality. We empirically evaluate the $\epsilon$-shotgun methods on a range of synthetic functions and two real-world problems, finding that they perform at least as well as state-of-the-art batch methods and in many cases exceed their performance.
The performance of acquisition functions for Bayesian optimisation to locate the global optimum of continuous functions is investigated in terms of the Pareto front between exploration and exploitation. We show that Expected Improvement (EI) and the Upper Confidence Bound (UCB) always select solutions to be expensively evaluated on the Pareto front, but Probability of Improvement is not guaranteed to do so and Weighted Expected Improvement does so only for a restricted range of weights. We introduce two novel $\epsilon$-greedy acquisition functions. Extensive empirical evaluation of these together with random search, purely exploratory, and purely exploitative search on 10 benchmark problems in 1 to 10 dimensions shows that $\epsilon$-greedy algorithms are generally at least as effective as conventional acquisition functions (e.g., EI and UCB), particularly with a limited budget. In higher dimensions $\epsilon$-greedy approaches are shown to have improved performance over conventional approaches. These results are borne out on a real world computational fluid dynamics optimisation problem and a robotics active learning problem. Our analysis and experiments suggest that the most effective strategy, particularly in higher dimensions, is to be mostly greedy, occasionally selecting a random exploratory solution.