In this work we introduce PHOENICS, a probabilistic global optimization algorithm combining ideas from Bayesian optimization with concepts from Bayesian kernel density estimation. We propose an inexpensive acquisition function balancing the explorative and exploitative behavior of the algorithm. This acquisition function enables intuitive sampling strategies for an efficient parallel search of global minima. The performance of PHOENICS is assessed via an exhaustive benchmark study on a set of 15 discrete, quasi-discrete and continuous multidimensional functions. Unlike optimization methods based on Gaussian processes (GP) and random forests (RF), we show that PHOENICS is less sensitive to the nature of the co-domain, and outperforms GP and RF optimizations. We illustrate the performance of PHOENICS on the Oregonator, a difficult case-study describing a complex chemical reaction network. We demonstrate that only PHOENICS was able to reproduce qualitatively and quantitatively the target dynamic behavior of this nonlinear reaction dynamics. We recommend PHOENICS for rapid optimization of scalar, possibly non-convex, black-box unknown objective functions.
Pohang University of Science and Technology（浦项科技大学）；BARO AI（巴罗人工智能公司）
Bayesian optimization is a sample-efficient method for finding a global optimum of an expensive-to-evaluate black-box function. A global solution is found by accumulating a pair of query point and its function value, repeating these two procedures: (i) modeling a surrogate function; (ii) maximizing an acquisition function to determine where next to query. Convergence guarantees are only valid when the global optimizer of the acquisition function is found at each round and selected as the next query point. In practice, however, local optimizers of an acquisition function are also used, since se…
The multi-level, multi-disciplinary and multi-fidelity optimization framework developed at Bombardier Aviation has shown great results to explore efficient and competitive aircraft configurations. This optimization framework has been developed within the Isight software, the latter offers a set of ready-to-use optimizers. Unfortunately, the computational effort required by the Isight optimizers can be prohibitive with respect to the requirements of an industrial context. In this paper, a constrained Bayesian optimization optimizer, namely the super efficient global optimization with mixture of…
University of Science and Technology of China（中国科学技术大学）
Bayesian optimization offers a flexible framework to optimize an objective function that is expensive to be evaluated. A Bayesian optimizer iteratively queries the function values on its carefully selected points. Subsequently, it makes a sensible recommendation about where the optimum locates based on its accumulated knowledge. This procedure usually demands a long execution time. In practice, however, there often exists a computational budget or an evaluation limitation allocated to an optimizer, due to the resource scarcity. This constraint demands an optimizer to be aware of its remaining …
We formulate the problem of neural network optimization as Bayesian filtering, where the observations are the backpropagated gradients. While neural network optimization has previously been studied using natural gradient methods which are closely related to Bayesian inference, they were unable to recover standard optimizers such as Adam and RMSprop with a root-mean-square gradient normalizer, instead getting a mean-square normalizer. To recover the root-mean-square normalizer, we find it necessary to account for the temporal dynamics of all the other parameters as they are geing optimized. The…
University of Toronto（多伦多大学）；Harvard University（哈佛大学）；Vector Institute for Artificial Intelligence（矢量人工智能研究所）；Atinary Technologies Inc（Atinary科技公司）；Canadian Institute for Advanced Research (CIFAR)（加拿大高级研究院）；Vector Institute（矢量研究所）
Bayesian optimization has emerged as a powerful strategy to accelerate scientific discovery by means of autonomous experimentation. However, expensive measurements are required to accurately estimate materials properties, and can quickly become a hindrance to exhaustive materials discovery campaigns. Here, we introduce Gemini: a data-driven model capable of using inexpensive measurements as proxies for expensive measurements by correcting systematic biases between property evaluation methods. We recommend using Gemini for regression tasks with sparse data and in an autonomous workflow setting …
Local Entropy Search over Descent Sequences for Bayesian Optimization
Institute for Data Science in Mechanical Engineering, RWTH Aachen University, Germany（机械工程数据科学研究所，亚琛工业大学，德国）；Learning Systems and Robotics Lab, Technical University of Munich, Germany（学习系统与机器人实验室，慕尼黑技术大学，德国）
Twitter（推特）；Facebook（脸书）；SigOpt, an Intel company（SigOpt（英特尔公司旗下））；Valohai；Paradigm（第四范式）；ChaLearn
This paper presents the results and insights from the black-box optimization (BBO) challenge at NeurIPS 2020 which ran from July-October, 2020. The challenge emphasized the importance of evaluating derivative-free optimizers for tuning the hyperparameters of machine learning models. This was the first black-box optimization challenge with a machine learning emphasis. It was based on tuning (validation set) performance of standard machine learning models on real datasets. This competition has widespread impact as black-box optimization (e.g., Bayesian optimization) is relevant for hyperparamete…
We extend the empirical results from the structural equation model (SEM) published in the paper Assortment Planning for Retail Buying, Retail Store Operations, and Firm Performance [1] by implementing the directed acyclic graph as a causal Bayesian neural network. Neural network convergence is shown to improve with the removal of the node with the weakest SEM path when variational inference is provided by perturbing weights with Flipout layers, while results from perturbing weights at the output with the Vadam optimizer are inconclusive.
ETH Zürich（苏黎世联邦理工学院）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Bosch Center for Artificial Intelligence（博世人工智能中心）；University of Freiburg（弗莱堡大学）
Transferring knowledge across tasks to improve data-efficiency is one of the open key challenges in the field of global black-box optimization. Readily available algorithms are typically designed to be universal optimizers and, therefore, often suboptimal for specific tasks. We propose a novel transfer learning method to obtain customized optimizers within the well-established framework of Bayesian optimization, allowing our algorithm to utilize the proven generalization capabilities of Gaussian processes. Using reinforcement learning to meta-train an acquisition function (AF) on a set of rela…
Looping in the Human Collaborative and Explainable Bayesian Optimization
University of Oxford（牛津大学）；Toyota Motor Corporation（丰田汽车公司）；The Faraday Institution（法拉第研究所）；CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）
Virginia Tech（弗吉尼亚理工大学）；Georgetown University（乔治城大学）
Bayesian optimization involves "inner optimization" over a new-data acquisition criterion which is non-convex/highly multi-modal, may be non-differentiable, or may otherwise thwart local numerical optimizers. In such cases it is common to replace continuous search with a discrete one over random candidates. Here we propose using candidates based on a Delaunay triangulation of the existing input design. We detail the construction of these "tricands" and demonstrate empirically how they outperform both numerically optimized acquisitions and random candidate-based alternatives, and are well-suite…
College of Engineering, Pune（浦那工程学院）；National Institute of Technology, Srinagar（斯利那加国家理工学院）
Bayesian Optimization is an effective method for searching the global maxima of an objective function especially if the function is unknown. The process comprises of using a surrogate function and choosing an acquisition function followed by optimizing the acquisition function to find the next sampling point. This paper analyzes different acquistion functions like Maximum Probability of Improvement and Expected Improvement and various optimizers like L-BFGS and TNC to optimize the acquisitions functions for finding the next sampling point. Along with the analysis of time taken, the paper also …
How should we intervene on an unknown structural equation model to maximize a downstream variable of interest? This setting, also known as causal Bayesian optimization (CBO), has important applications in medicine, ecology, and manufacturing. Standard Bayesian optimization algorithms fail to effectively leverage the underlying causal structure. Existing CBO approaches assume noiseless measurements and do not come with guarantees. We propose the model-based causal Bayesian optimization algorithm (MCBO) that learns a full system model instead of only modeling intervention-reward pairs. MCBO prop…
Department of Statistics（统计系）；INSPER；Chicago Booth（芝加哥布斯商学院）；University of Chicago（芝加哥大学）；Volgenau School of Engineering（沃尔格瑙工程学院）；George Mason University（乔治梅森大学）
University of Oxford（牛津大学）；Uber AI（优步人工智能实验室）；University of Michigan（密歇根大学）
We introduce a fully stochastic gradient based approach to Bayesian optimal experimental design (BOED). Our approach utilizes variational lower bounds on the expected information gain (EIG) of an experiment that can be simultaneously optimized with respect to both the variational and design parameters. This allows the design process to be carried out through a single unified stochastic gradient ascent procedure, in contrast to existing approaches that typically construct a pointwise EIG estimator, before passing this estimator to a separate optimizer. We provide a number of different variation…
BayzAI；Volkswagen Group of America（美国大众汽车集团）；Innovation Center California（加州创新中心）
Finding methods for making generalizable predictions is a fundamental problem of machine learning. By looking into similarities between the prediction problem for unknown data and the lossless compression we have found an approach that gives a solution. In this paper we propose a compression principle that states that an optimal predictive model is the one that minimizes a total compressed message length of all data and model definition while guarantees decodability. Following the compression principle we use Bayesian approach to build probabilistic models of data and network definitions. A me…
Ludwig-Maximilians-Universität München（慕尼黑大学）；University of Wyoming（怀俄明大学）
Automated hyperparameter optimization (HPO) has gained great popularity and is an important ingredient of most automated machine learning frameworks. The process of designing HPO algorithms, however, is still an unsystematic and manual process: Limitations of prior work are identified and the improvements proposed are -- even though guided by expert knowledge -- still somewhat arbitrary. This rarely allows for gaining a holistic understanding of which algorithmic components are driving performance, and carries the risk of overlooking good algorithmic design choices. We present a principled app…
Physico-chemical continuum battery models are typically parameterized by manual fits, relying on the individual expertise of researchers. In this article, we introduce a computer algorithm that directly utilizes the experience of battery researchers to extract information from experimental data reproducibly. We extend Bayesian Optimization (BOLFI) with Expectation Propagation (EP) to create a black-box optimizer suited for modular continuum battery models. Standard approaches compare the experimental data in its raw entirety to the model simulations. By dividing the data into physics-based fea…
Bayesian Optimization has become the reference method for the global optimization of black box, expensive and possibly noisy functions. Bayesian Op-timization learns a probabilistic model about the objective function, usually a Gaussian Process, and builds, depending on its mean and variance, an acquisition function whose optimizer yields the new evaluation point, leading to update the probabilistic surrogate model. Despite its sample efficiency, Bayesian Optimiza-tion does not scale well with the dimensions of the problem. The optimization of the acquisition function has received less attenti…
In the machine learning algorithms, the choice of the hyperparameter is often an art more than a science, requiring labor-intensive search with expert experience. Therefore, automation on hyperparameter optimization to exclude human intervention is a great appeal, especially for the black-box functions. Recently, there have been increasing demands of solving such concealed tasks for better generalization, though the task-dependent issue is not easy to solve. The Black-Box Optimization challenge (NeurIPS 2020) required competitors to build a robust black-box optimizer across different domains o…
University of Edinburgh（爱丁堡大学）；School of Informatics（信息学院）；School of Engineering（工程学院）
Recently, different machine learning methods have been introduced to tackle the challenging few-shot learning scenario that is, learning from a small labeled dataset related to a specific task. Common approaches have taken the form of meta-learning: learning to learn on the new problem given the old. Following the recognition that meta-learning is implementing learning in a multi-level model, we present a Bayesian treatment for the meta-learning inner loop through the use of deep kernels. As a result we can learn a kernel that transfers to new tasks; we call this Deep Kernel Transfer (DKT). Th…
We present mlrMBO, a flexible and comprehensive R toolbox for model-based optimization (MBO), also known as Bayesian optimization, which addresses the problem of expensive black-box optimization by approximating the given objective function through a surrogate regression model. It is designed for both single- and multi-objective optimization with mixed continuous, categorical and conditional parameters. Additional features include multi-point batch proposal, parallelization, visualization, logging and error-handling. mlrMBO is implemented in a modular fashion, such that single components can b…
Ludwig-Maximilians-Universität München（慕尼黑大学）；Leibniz University Hannover（汉诺威莱布尼茨大学）
Despite all the benefits of automated hyperparameter optimization (HPO), most modern HPO algorithms are black-boxes themselves. This makes it difficult to understand the decision process which leads to the selected configuration, reduces trust in HPO, and thus hinders its broad adoption. Here, we study the combination of HPO with interpretable machine learning (IML) methods such as partial dependence plots. These techniques are more and more used to explain the marginal effect of hyperparameters on the black-box cost function or to quantify the importance of hyperparameters. However, if such m…
The lottery ticket hypothesis (LTH) has attracted attention because it can explain why over-parameterized models often show high generalization ability. It is known that when we use iterative magnitude pruning (IMP), which is an algorithm to find sparse networks with high generalization ability that can be trained from the initial weights independently, called winning tickets, the initial large learning rate does not work well in deep neural networks such as ResNet. However, since the initial large learning rate generally helps the optimizer to converge to flatter minima, we hypothesize that t…
Delft University of Technology（代尔夫特理工大学）；Tsinghua University（清华大学）；ABB Research（ABB研究院）
Noisy labeled data is more a norm than a rarity for crowd sourced contents. It is effective to distill noise and infer correct labels through aggregation results from crowd workers. To ensure the time relevance and overcome slow responses of workers, online label aggregation is increasingly requested, calling for solutions that can incrementally infer true label distribution via subsets of data items. In this paper, we propose a novel online label aggregation framework, BiLA, which employs variational Bayesian inference method and designs a novel stochastic optimization scheme for incremental …
New York University（纽约大学）；BigHat Biosciences（BigHat生物科学公司）
Bayesian optimization (BayesOpt) is a gold standard for query-efficient continuous optimization. However, its adoption for drug design has been hindered by the discrete, high-dimensional nature of the decision variables. We develop a new approach (LaMBO) which jointly trains a denoising autoencoder with a discriminative multi-task Gaussian process head, allowing gradient-based optimization of multi-objective acquisition functions in the latent space of the autoencoder. These acquisition functions allow LaMBO to balance the explore-exploit tradeoff over multiple design rounds, and to balance ob…
Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially updated by new function evaluations. An acquisition strategy uses this posterior distribution to decide where to place the next function evaluation. We propose a novel Bayesian optimization framework for situations where the user controls the computational effort, and therefore the precision of the function evaluations. This is a common situation in econome…
RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；University of British Columbia（不列颠哥伦比亚大学）；University of Oxford（牛津大学）；University of Edinburgh（爱丁堡大学）
Uncertainty computation in deep learning is essential to design robust and reliable systems. Variational inference (VI) is a promising approach for such computation, but requires more effort to implement and execute compared to maximum-likelihood methods. In this paper, we propose new natural-gradient algorithms to reduce such efforts for Gaussian mean-field VI. Our algorithms can be implemented within the Adam optimizer by perturbing the network weights during gradient evaluations, and uncertainty estimates can be cheaply obtained by using the vector that adapts the learning rate. This requir…
The University of Sydney（悉尼大学）；College of Control Science and Engineering, China University of Petroleum (East China)（中国石油大学（华东）控制科学与工程学院）；Shanghai Jiao Tong University（上海交通大学）；JD Explore Academy（京东探索研究院）
It is commonly believed that Bayesian optimization (BO) algorithms are highly efficient for optimizing numerically costly functions. However, BO is not often compared to widely different alternatives, and is mostly tested on narrow sets of problems (multimodal, low-dimensional functions), which makes it difficult to assess where (or if) they actually achieve state-of-the-art performance. Moreover, several aspects in the design of these algorithms vary across implementations without a clear recommendation emerging from current practices, and many of these design choices are not substantiated by…
A PAC-Bayesian Perspective on the Interpolating Information Criterion
University of Melbourne（墨尔本大学）；Queensland University of Technology（昆士兰理工大学）；University of Queensland（昆士兰大学）；University of California, Berkeley（加州大学伯克利分校）
Most real optimization problems are defined over a mixed search space where the variables are both discrete and continuous. In engineering applications, the objective function is typically calculated with a numerically costly black-box simulation.General mixed and costly optimization problems are therefore of a great practical interest, yet their resolution remains in a large part an open scientific question. In this article, costly mixed problems are approached through Gaussian processes where the discrete variables are relaxed into continuous latent variables. The continuous space is more ea…
When the infection prevalence of a disease is low, Dorfman showed 80 years ago that testing groups of people can prove more efficient than testing people individually. Our goal in this paper is to propose new group testing algorithms that can operate in a noisy setting (tests can be mistaken) to decide adaptively (looking at past results) which groups to test next, with the goal to converge to a good detection, as quickly, and with as few tests as possible. We cast this problem as a Bayesian sequential experimental design problem. Using the posterior distribution of infection status vectors fo…
