Hyperparameter optimization and neural architecture search can become prohibitively expensive for regular black-box Bayesian optimization because the training and evaluation of a single model can easily take several hours. To overcome this, we introduce a comprehensive tool suite for effective multi-fidelity Bayesian optimization and the analysis of its runs. The suite, written in Python, provides a simple way to specify complex design spaces, a robust and efficient combination of Bayesian optimization and HyperBand, and a comprehensive analysis of the optimization process and its outcomes.
With the surge in the number of hyperparameters and training times of modern machine learning models, hyperparameter tuning is becoming increasingly expensive. However, after assessing 40 tuning methods systematically, we find that each faces certain limitations. In particular, methods that speed up tuning via knowledge transfer typically require the final performance of hyperparameters and do not focus on low-fidelity information. As we demonstrate empirically, this common practice is suboptimal and can incur an unnecessary use of resources. It is more cost-efficient to instead leverage low-f…
Bayesian optimization is popular for optimizing time-consuming black-box objectives. Nonetheless, for hyperparameter tuning in deep neural networks, the time required to evaluate the validation error for even a few hyperparameter settings remains a bottleneck. Multi-fidelity optimization promises relief using cheaper proxies to such objectives --- for example, validation error for a network trained using a subset of the training points or fewer iterations than required for convergence. We propose a highly flexible and practical approach to multi-fidelity Bayesian optimization, focused on effic…
Bayesian Optimization of Genetic Algorithm Hyperparameters in a Multi-Fidelity Framework for Efficient Lattice Material Design
IMDEA Materials Institute（IMDEA材料研究所）；Department of Materials Science and Engineering and Chemical Engineering（材料科学与工程及化学工程系）；Universidad Carlos III de Madrid（马德里卡洛斯三世大学）
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…
Amazon Web Services（亚马逊云科技）；University of Sydney（悉尼大学）
We introduce a model-based asynchronous multi-fidelity method for hyperparameter and neural architecture search that combines the strengths of asynchronous Hyperband and Gaussian process-based Bayesian optimization. At the heart of our method is a probabilistic model that can simultaneously reason across hyperparameters and resource levels, and supports decision-making in the presence of pending evaluations. We demonstrate the effectiveness of our method on a wide range of challenging benchmarks, for tabular data, image classification and language modelling, and report substantial speed-ups ov…
Carnegie Mellon University（卡内基梅隆大学）；University of Washington（华盛顿大学）；Google Research（谷歌研究院）；Determined AI
Performance of machine learning algorithms depends critically on identifying a good set of hyperparameters. While recent approaches use Bayesian optimization to adaptively select configurations, we focus on speeding up random search through adaptive resource allocation and early-stopping. We formulate hyperparameter optimization as a pure-exploration non-stochastic infinite-armed bandit problem where a predefined resource like iterations, data samples, or features is allocated to randomly sampled configurations. We introduce a novel algorithm, Hyperband, for this framework and analyze its theo…
In this work, we propose a new Gaussian process regression (GPR)-based multifidelity method: physics-informed CoKriging (CoPhIK). In CoKriging-based multifidelity methods, the quantities of interest are modeled as linear combinations of multiple parameterized stationary Gaussian processes (GPs), and the hyperparameters of these GPs are estimated from data via optimization. In CoPhIK, we construct a GP representing low-fidelity data using physics-informed Kriging (PhIK), and model the discrepancy between low- and high-fidelity data using a parameterized GP with hyperparameters identified via op…
Gaussian process regression is a popular method for non-parametric probabilistic modeling of functions. The Gaussian process prior is characterized by so-called hyperparameters, which often have a large influence on the posterior model and can be difficult to tune. This work provides a method for numerical marginalization of the hyperparameters, relying on the rigorous framework of sequential Monte Carlo. Our method is well suited for online problems, and we demonstrate its ability to handle real-world problems with several dimensions and compare it to other marginalization methods. We also co…
Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective. This classical approach known as Type-II maximum likelihood (ML-II) yields point estimates of the hyperparameters, and continues to be the default method for training GPs. However, this approach risks underestimating predictive uncertainty and is prone to overfitting especially when there are many hyperparameters. Furthermore, gradient based optimisation make…
On Some Tunable Multi-fidelity Bayesian Optimization Frameworks
Department of Chemical and Biomolecular Engineering, Johns Hopkins University, U.S.A.（化学与生物分子工程系，约翰霍普金斯大学，美国）；Department of Civil and Systems Engineering, Johns Hopkins University, U.S.A.（土木与系统工程系，约翰霍普金斯大学，美国）；Department of Mechanical Engineering, Massachusetts Institute of Technology, U.S.A.（机械工程系，麻省理工学院，美国）
Bayesian optimization (BO) has become a popular strategy for global optimization of many expensive real-world functions. Contrary to a common belief that BO is suited to optimizing black-box functions, it actually requires domain knowledge on characteristics of those functions to deploy BO successfully. Such domain knowledge often manifests in Gaussian process priors that specify initial beliefs on functions. However, even with expert knowledge, it is not an easy task to select a prior. This is especially true for hyperparameter tuning problems on complex machine learning models, where landsca…
Bayesian optimization (BO) is a powerful approach for optimizing black-box, expensive-to-evaluate functions. To enable a flexible trade-off between the cost and accuracy, many applications allow the function to be evaluated at different fidelities. In order to reduce the optimization cost while maximizing the benefit-cost ratio, in this paper, we propose Batch Multi-fidelity Bayesian Optimization with Deep Auto-Regressive Networks (BMBO-DARN). We use a set of Bayesian neural networks to construct a fully auto-regressive model, which is expressive enough to capture strong yet complex relationsh…
Rutgers University（罗格斯大学）；Institute for Advanced Study（普林斯顿高等研究院）
Deep Gaussian Processes (DGPs) were proposed as an expressive Bayesian model capable of a mathematically grounded estimation of uncertainty. The expressivity of DPGs results from not only the compositional character but the distribution propagation within the hierarchy. Recently, [1] pointed out that the hierarchical structure of DGP well suited modeling the multi-fidelity regression, in which one is provided sparse observations with high precision and plenty of low fidelity observations. We propose the conditional DGP model in which the latent GPs are directly supported by the fixed lower fid…
Sparse pseudo-point approximations for Gaussian process (GP) models provide a suite of methods that support deployment of GPs in the large data regime and enable analytic intractabilities to be sidestepped. However, the field lacks a principled method to handle streaming data in which both the posterior distribution over function values and the hyperparameter estimates are updated in an online fashion. The small number of existing approaches either use suboptimal hand-crafted heuristics for hyperparameter learning, or suffer from catastrophic forgetting or slow updating when new data arrive. T…
When developing and analyzing new hyperparameter optimization methods, it is vital to empirically evaluate and compare them on well-curated benchmark suites. In this work, we propose a new set of challenging and relevant benchmark problems motivated by desirable properties and requirements for such benchmarks. Our new surrogate-based benchmark collection consists of 14 scenarios that in total constitute over 700 multi-fidelity hyperparameter optimization problems, which all enable multi-objective hyperparameter optimization. Furthermore, we empirically compare surrogate-based benchmarks to the…
In black-box optimization problems, we aim to maximize an unknown objective function, where the function is only accessible through feedbacks of an evaluation or simulation oracle. In real-life, the feedbacks of such oracles are often noisy and available after some unknown delay that may depend on the computation time of the oracle. Additionally, if the exact evaluations are expensive but coarse approximations are available at a lower cost, the feedbacks can have multi-fidelity. In order to address this problem, we propose a generic extension of hierarchical optimistic tree search (HOO), calle…
Despite the evolution of Convolutional Neural Networks (CNNs), their performance is surprisingly dependent on the choice of hyperparameters. However, it remains challenging to efficiently explore large hyperparameter search space due to the long training times of modern CNNs. Multi-fidelity optimization enables the exploration of more hyperparameter configurations given budget by early termination of unpromising configurations. However, it often results in selecting a sub-optimal configuration as training with the high-performing configuration typically converges slowly in an early phase. In t…
Centre Tecnològic de Telecomunicacions de Catalunya（加泰罗尼亚电信技术中心）；Aalborg University（奥尔堡大学）；LUT University（拉彭兰塔工业大学）
In this paper, a hyperparameter tuning based Bayesian optimization of digital twins is carried out to diagnose various faults in grid connected inverters. As fault detection and diagnosis require very high precision, we channelize our efforts towards an online optimization of the digital twins, which, in turn, allows a flexible implementation with limited amount of data. As a result, the proposed framework not only becomes a practical solution for model versioning and deployment of digital twins design with limited data, but also allows integration of deep learning tools to improve the hyperpa…
SigOpt: An Intel Company（SigOpt（英特尔旗下公司））；Facebook（脸书）；Amazon（亚马逊）
Bayesian optimization (BO) is a popular method for optimizing expensive-to-evaluate black-box functions. BO budgets are typically given in iterations, which implicitly assumes each evaluation has the same cost. In fact, in many BO applications, evaluation costs vary significantly in different regions of the search space. In hyperparameter optimization, the time spent on neural network training increases with layer size; in clinical trials, the monetary cost of drug compounds vary; and in optimal control, control actions have differing complexities. Cost-constrained BO measures convergence with…
Hyperparameter optimization (HPO) is a fundamental problem in automatic machine learning (AutoML). However, due to the expensive evaluation cost of models (e.g., training deep learning models or training models on large datasets), vanilla Bayesian optimization (BO) is typically computationally infeasible. To alleviate this issue, Hyperband (HB) utilizes the early stopping mechanism to speed up configuration evaluations by terminating those badly-performing configurations in advance. This leads to two kinds of quality measurements: (1) many low-fidelity measurements for configurations that get …
Searching for accurate Machine and Deep Learning models is a computationally expensive and awfully energivorous process. A strategy which has been gaining recently importance to drastically reduce computational time and energy consumed is to exploit the availability of different information sources, with different computational costs and different "fidelity", typically smaller portions of a large dataset. The multi-source optimization strategy fits into the scheme of Gaussian Process based Bayesian Optimization. An Augmented Gaussian Process method exploiting multiple information sources (name…
Hyperparameter optimization (HPO) is crucial for machine learning algorithms to achieve satisfactory performance, whose progress has been boosted by related benchmarks. Nonetheless, existing efforts in benchmarking all focus on HPO for traditional centralized learning while ignoring federated learning (FL), a promising paradigm for collaboratively learning models from dispersed data. In this paper, we first identify some uniqueness of HPO for FL algorithms from various aspects. Due to this uniqueness, existing HPO benchmarks no longer satisfy the need to compare HPO methods in the FL setting. …
Multi-fidelity Kriging model is a promising technique in surrogate-based design as it can balance the model accuracy and cost of sample preparation by fusing low- and high-fidelity data. However, the cost for building a multi-fidelity Kriging model increases significantly with the increase of the problem dimension. To attack this issue, an efficient Hierarchical Kriging modeling method is proposed. In building the low-fidelity model, the maximal information coefficient is utilized to calculate the relative value of the hyperparameter. With this, the maximum likelihood estimation problem for de…
Efficient Hyperparameter Optimization for LLM Reinforcement Learning
The Hong Kong University of Science and Technology (Guangzhou)（香港科学与技术大学（广州））；The Hong Kong University of Science and Technology（香港科学与技术大学）；China United Network Communications Group（中国联合网络通信集团）
Lund University（隆德大学）；Université Paris-Saclay（巴黎萨克雷大学）；Inria（法国国家信息与自动化研究所）；CEA（法国原子能和替代能源委员会）；Université de Montpellier（蒙彼利埃大学）；CNRS（法国国家科学研究中心）；Institut Universitaire de France (IUF)（法国大学研究院）；Stanford University（斯坦福大学）
While Weighted Lasso sparse regression has appealing statistical guarantees that would entail a major real-world impact in finance, genomics, and brain imaging applications, it is typically scarcely adopted due to its complex high-dimensional space composed by thousands of hyperparameters. On the other hand, the latest progress with high-dimensional hyperparameter optimization (HD-HPO) methods for black-box functions demonstrates that high-dimensional applications can indeed be efficiently optimized. Despite this initial success, HD-HPO approaches are mostly applied to synthetic problems with …
University of Freiburg（弗莱堡大学）；Leibniz University Hannover（莱布尼茨汉诺威大学）；Bosch Center for Artificial Intelligence（博世人工智能中心）
While early AutoML frameworks focused on optimizing traditional ML pipelines and their hyperparameters, a recent trend in AutoML is to focus on neural architecture search. In this paper, we introduce Auto-PyTorch, which brings the best of these two worlds together by jointly and robustly optimizing the architecture of networks and the training hyperparameters to enable fully automated deep learning (AutoDL). Auto-PyTorch achieves state-of-the-art performance on several tabular benchmarks by combining multi-fidelity optimization with portfolio construction for warmstarting and ensembling of dee…
Physics-based character animation has seen significant advances in recent years with the adoption of Deep Reinforcement Learning (DRL). However, DRL-based learning methods are usually computationally expensive and their performance crucially depends on the choice of hyperparameters. Tuning hyperparameters for these methods often requires repetitive training of control policies, which is even more computationally prohibitive. In this work, we propose a novel Curriculum-based Multi-Fidelity Bayesian Optimization framework (CMFBO) for efficient hyperparameter optimization of DRL-based character c…
Multi-fidelity Bayesian Data-Driven Design of Energy Absorbing Spinodoid Cellular Structures
Department of Electronic Components, Technology and Materials, Delft University of Technology（电子组件、技术和材料系，代尔夫特理工大学）；School of Engineering and Materials Science, Queen Mary University of London（工程与材料科学学院，伦敦女王学院）
Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions and enables us to evaluate both the model parameters and hyperparameters probabilistically by the joint posterior. However, even in a linear inverse problem, it is unsolved how we should extract useful information on the model parameters from the joint posterior. This study presents a theoretical exploration into the appropriate dimensionality reduction of …
Motivated by the task of hyperparameter optimization, we introduce the non-stochastic best-arm identification problem. Within the multi-armed bandit literature, the cumulative regret objective enjoys algorithms and analyses for both the non-stochastic and stochastic settings while to the best of our knowledge, the best-arm identification framework has only been considered in the stochastic setting. We introduce the non-stochastic setting under this framework, identify a known algorithm that is well-suited for this setting, and analyze its behavior. Next, by leveraging the iterative nature of s…
XGBoost, a scalable tree boosting algorithm, has proven effective for many prediction tasks of practical interest, especially using tabular datasets. Hyperparameter tuning can further improve the predictive performance, but unlike neural networks, full-batch training of many models on large datasets can be time consuming. Owing to the discovery that (i) there is a strong linear relation between dataset size & training time, (ii) XGBoost models satisfy the ranking hypothesis, and (iii) lower-fidelity models can discover promising hyperparameter configurations, we show that uniform subsampling m…
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
The Generative Adversarial Network (GAN) is a powerful and flexible tool that can generate high-fidelity synthesized data by learning. It has seen many applications in simulating events in High Energy Physics (HEP), including simulating detector responses and physics events. However, training GANs is notoriously hard and optimizing their hyperparameters even more so. It normally requires many trial-and-error training attempts to force a stable training and reach a reasonable fidelity. Significant tuning work has to be done to achieve the accuracy required by physics analyses. This work uses th…
Knowledge graph embedding (KGE) models are an effective and popular approach to represent and reason with multi-relational data. Prior studies have shown that KGE models are sensitive to hyperparameter settings, however, and that suitable choices are dataset-dependent. In this paper, we explore hyperparameter optimization (HPO) for very large knowledge graphs, where the cost of evaluating individual hyperparameter configurations is excessive. Prior studies often avoided this cost by using various heuristics; e.g., by training on a subgraph or by using fewer epochs. We systematically discuss an…
Provably Reduced Sample Cost in Prior-Guided Hyperparameter Optimization
Leibniz University Hanover（莱比锡大学汉诺威分校）；University of Bielefeld（比勒菲尔德大学）；Institute of Artificial Intelligence, Leibniz University Hanover（人工智能研究所，莱比锡大学汉诺威分校）；L3S Research Center Hanover（汉诺威L3S研究中心）
Tree-based Learning for High-Fidelity Prediction of Chaos
School of Mathematics and Statistics（数学与统计学学院）；Rochester Institute of Technology（罗切斯特理工学院）；Chester F. Carlson Center for Imaging Science（Chester F. Carlson 成像科学中心）；Clarkson Center for Complex Systems Science（Clarkson 复杂系统科学中心）；Clarkson University（Clarkson 大学）；Department of Electrical and Computer Engineering（电气与计算机工程系）
