Recurrent neural networks (RNNs) are a powerful approach for time series prediction. However, their performance is strongly affected by their architecture and hyperparameter settings. The architecture optimization of RNNs is a time-consuming task, where the search space is typically a mixture of real, integer and categorical values. To allow for shrinking and expanding the size of the network, the representation of architectures often has a variable length. In this paper, we propose to tackle the architecture optimization problem with a variant of the Bayesian Optimization (BO) algorithm. To reduce the evaluation time of candidate architectures the Mean Absolute Error Random Sampling (MRS), a training-free method to estimate the network performance, is adopted as the objective function for BO. Also, we propose three fixed-length encoding schemes to cope with the variable-length architecture representation. The result is a new perspective on accurate and efficient design of RNNs, that we validate on three problems. Our findings show that 1) the BO algorithm can explore different network architectures using the proposed encoding schemes and successfully designs well-performing architectures, and 2) the optimization time is significantly reduced by using MRS, without compromising the performance as compared to the architectures obtained from the actual training procedure.
University of California at Los Angeles（加州大学洛杉矶分校）
Approaches to learning Bayesian networks from data typically combine a scoring function with a heuristic search procedure. Given a Bayesian network structure, many of the scoring functions derived in the literature return a score for the entire equivalence class to which the structure belongs. When using such a scoring function, it is appropriate for the heuristic search algorithm to search over equivalence classes of Bayesian networks as opposed to individual structures. We present the general formulation of a search space for which the states of the search correspond to equivalence classes o…
Machine learning pipeline potentially consists of several stages of operations like data preprocessing, feature engineering and machine learning model training. Each operation has a set of hyper-parameters, which can become irrelevant for the pipeline when the operation is not selected. This gives rise to a hierarchical conditional hyper-parameter space. To optimize this mixed continuous and discrete conditional hierarchical hyper-parameter space, we propose an efficient pipeline search and configuration algorithm which combines the power of Reinforcement Learning and Bayesian Optimization. Em…
Over the past half-decade, many methods have been considered for neural architecture search (NAS). Bayesian optimization (BO), which has long had success in hyperparameter optimization, has recently emerged as a very promising strategy for NAS when it is coupled with a neural predictor. Recent work has proposed different instantiations of this framework, for example, using Bayesian neural networks or graph convolutional networks as the predictive model within BO. However, the analyses in these papers often focus on the full-fledged NAS algorithm, so it is difficult to tell which individual com…
Kobe Steel, Ltd.（神户制钢所）；The Institute of Statistical Mathematics（统计数理研究所）；RIKEN AIP（理化学研究所AIP）
Bayesian optimization is an effective method to efficiently optimize unknown objective functions with high evaluation costs. Traditional Bayesian optimization algorithms select one point per iteration for single objective function, whereas in recent years, Bayesian optimization for multi-objective optimization or multi-point search per iteration have been proposed. However, Bayesian optimization that can deal with them at the same time in non-heuristic way is not known at present. We propose a Bayesian optimization algorithm that can deal with multi-objective optimization and multi-point searc…
Bosch Center for Artificial Intelligence（博世人工智能中心）
Despite recent advances in automated machine learning, model selection is still a complex and computationally intensive process. For Gaussian processes (GPs), selecting the kernel is a crucial task, often done manually by the expert. Additionally, evaluating the model selection criteria for Gaussian processes typically scales cubically in the sample size, rendering kernel search particularly computationally expensive. We propose a novel, efficient search method through a general, structured kernel space. Previous methods solved this task via Bayesian optimization and relied on measuring the di…
Jilin University（吉林大学）；Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education（教育部符号计算与知识工程重点实验室）
Bayesian optimization (BO) is an effective method of finding the global optima of black-box functions. Recently BO has been applied to neural architecture search and shows better performance than pure evolutionary strategies. All these methods adopt Gaussian processes (GPs) as surrogate function, with the handcraft similarity metrics as input. In this work, we propose a Bayesian graph neural network as a new surrogate, which can automatically extract features from deep neural architectures, and use such learned features to fit and characterize black-box objectives and their uncertainty. Based …
Recently several researchers have investigated techniques for using data to learn Bayesian networks containing compact representations for the conditional probability distributions (CPDs) stored at each node. The majority of this work has concentrated on using decision-tree representations for the CPDs. In addition, researchers typically apply non-Bayesian (or asymptotically Bayesian) scoring functions such as MDL to evaluate the goodness-of-fit of networks to the data. In this paper we investigate a Bayesian approach to learning Bayesian networks that contain the more general decision-graph r…
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）
Shanghai Jiao Tong University（上海交通大学）；University of Birmingham（伯明翰大学）
Global optimization finds applications in a wide range of real world problems. The multi-start methods are a popular class of global optimization techniques, which are based on the ideas of conducting local searches at multiple starting points. In this work we propose a new multi-start algorithm where the starting points are determined in a Bayesian optimization framework. Specifically, the method can be understood as to construct a new function by conducting local searches of the original objective function, where the new function attains the same global optima as the original one. Bayesian o…
In this paper we propose a Bayesian method for estimating architectural parameters of neural networks, namely layer size and network depth. We do this by learning concrete distributions over these parameters. Our results show that regular networks with a learnt structure can generalise better on small datasets, while fully stochastic networks can be more robust to parameter initialisation. The proposed method relies on standard neural variational learning and, unlike randomised architecture search, does not require a retraining of the model, thus keeping the computational overhead at minimum.
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 …
Bosch Center for AI（博世人工智能中心）；Idiap Research Institute（Idiap研究院）；National University of Singapore（新加坡国立大学）；University of Cambridge（剑桥大学）
Scarce data is a major challenge to scaling robot learning to truly complex tasks, as we need to generalize locally learned policies over different task contexts. Contextual policy search offers data-efficient learning and generalization by explicitly conditioning the policy on a parametric context space. In this paper, we further structure the contextual policy representation. We propose to factor contexts into two components: target contexts that describe the task objectives, e.g. target position for throwing a ball; and environment contexts that characterize the environment, e.g. initial po…
Univ. of Economics Prague（布拉格经济大学）；University of Utrecht（乌得勒支大学）
The search space of Bayesian Network structures is usually defined as Acyclic Directed Graphs (DAGs) and the search is done by local transformations of DAGs. But the space of Bayesian Networks is ordered by DAG Markov model inclusion and it is natural to consider that a good search policy should take this into account. First attempt to do this (Chickering 1996) was using equivalence classes of DAGs instead of DAGs itself. This approach produces better results but it is significantly slower. We present a compromise between these two approaches. It uses DAGs to search the space in such a way tha…
Scarce data is a major challenge to scaling robot learning to truly complex tasks, as we need to generalize locally learned policies over different "contexts". Bayesian optimization approaches to contextual policy search (CPS) offer data-efficient policy learning that generalize over a context space. We propose to improve data-efficiency by factoring typically considered contexts into two components: target-type contexts that correspond to a desired outcome of the learned behavior, e.g. target position for throwing a ball; and environment type contexts that correspond to some state of the envi…
University of Crete（克里特大学）；Institute of Computer Science, FORTH（希腊研究与技术基金会计算机科学研究所）
A significant theoretical advantage of search-and-score methods for learning Bayesian Networks is that they can accept informative prior beliefs for each possible network, thus complementing the data. In this paper, a method is presented for assigning priors based on beliefs on the presence or absence of certain paths in the true network. Such beliefs correspond to knowledge about the possible causal and associative relations between pairs of variables. This type of knowledge naturally arises from prior experimental and observational data, among others. In addition, a novel search-operator is …
The aim of black-box optimization is to optimize an objective function within the constraints of a given evaluation budget. In this problem, it is generally assumed that the computational cost for evaluating a point is large; thus, it is important to search efficiently with as low budget as possible. Bayesian optimization is an efficient method for black-box optimization and provides exploration-exploitation trade-off by constructing a surrogate model that considers uncertainty of the objective function. However, because Bayesian optimization should construct the surrogate model for the entire…
One of the basic tasks for Bayesian networks (BNs) is that of learning a network structure from data. The BN-learning problem is NP-hard, so the standard solution is heuristic search. Many approaches have been proposed for this task, but only a very small number outperform the baseline of greedy hill-climbing with tabu lists; moreover, many of the proposed algorithms are quite complex and hard to implement. In this paper, we propose a very simple and easy-to-implement method for addressing this task. Our approach is based on the well-known fact that the best network (of bounded in-degree) cons…
Entropy Search (ES) and Predictive Entropy Search (PES) are popular and empirically successful Bayesian Optimization techniques. Both rely on a compelling information-theoretic motivation, and maximize the information gained about the $\arg\max$ of the unknown function; yet, both are plagued by the expensive computation for estimating entropies. We propose a new criterion, Max-value Entropy Search (MES), that instead uses the information about the maximum function value. We show relations of MES to other Bayesian optimization methods, and establish a regret bound. We observe that MES maintains…
In practical Bayesian optimization, we must often search over structures with differing numbers of parameters. For instance, we may wish to search over neural network architectures with an unknown number of layers. To relate performance data gathered for different architectures, we define a new kernel for conditional parameter spaces that explicitly includes information about which parameters are relevant in a given structure. We show that this kernel improves model quality and Bayesian optimization results over several simpler baseline kernels.
We are often interested in identifying the feasible subset of a decision space under multiple constraints to permit effective design exploration. If determining feasibility required computationally expensive simulations, the cost of exploration would be prohibitive. Bayesian search is data-efficient for such problems: starting from a small dataset, the central concept is to use Bayesian models of constraints with an acquisition function to locate promising solutions that may improve predictions of feasibility when the dataset is augmented. At the end of this sequential active learning approach…
Lund University（隆德大学）；University of Freiburg（弗赖堡大学）；Bosch Center for Artificial Intelligence（博世人工智能中心）；Stanford University（斯坦福大学）；DBtune（DBtune公司）
Information-theoretic Bayesian optimization techniques have become popular for optimizing expensive-to-evaluate black-box functions due to their non-myopic qualities. Entropy Search and Predictive Entropy Search both consider the entropy over the optimum in the input space, while the recent Max-value Entropy Search considers the entropy over the optimal value in the output space. We propose Joint Entropy Search (JES), a novel information-theoretic acquisition function that considers an entirely new quantity, namely the entropy over the joint optimal probability density over both input and outp…
In large domains, Monte-Carlo tree search (MCTS) is required to estimate the values of the states as efficiently and accurately as possible. However, the standard update rule in backpropagation assumes a stationary distribution for the returns, and particularly in min-max trees, convergence to the true value can be slow because of averaging. We present two methods, Softmax MCTS and Monotone MCTS, which generalize previous attempts to improve upon the backpropagation strategy. We demonstrate that both methods reduce to finding optimal monotone functions, which we do so by performing Bayesian op…
NOVA LINCS（NOVA LINCS 实验室）；Universidade da Beira Interior（贝拉内政大学）
Neural Architecture Search has achieved state-of-the-art performance in a variety of tasks, out-performing human-designed networks. However, many assumptions, that require human definition, related with the problems being solved or the models generated are still needed: final model architectures, number of layers to be sampled, forced operations, small search spaces, which ultimately contributes to having models with higher performances at the cost of inducing bias into the system. In this paper, we propose HMCNAS, which is composed of two novel components: i) a method that leverages informati…
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…
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…
Hebrew University（希伯来大学）；Institute of Computer Science（计算机科学研究所）；Center for Neural Computations（神经计算中心）
Learning Bayesian networks is often cast as an optimization problem, where the computational task is to find a structure that maximizes a statistically motivated score. By and large, existing learning tools address this optimization problem using standard heuristic search techniques. Since the search space is extremely large, such search procedures can spend most of the time examining candidates that are extremely unreasonable. This problem becomes critical when we deal with data sets that are large either in the number of instances, or the number of attributes. In this paper, we introduce an …
The graph structure of a Bayesian network (BN) can be learned from data using the well-known score-and-search approach. Previous work has shown that incorporating structured representations of the conditional probability distributions (CPDs) into the score-and-search approach can improve the accuracy of the learned graph. In this paper, we present a novel approach capable of learning the graph of a BN and simultaneously modelling linear and non-linear local probabilistic relationships between variables. We achieve this by a combination of feature selection to reduce the search space for local …
Delft University of Technology（代尔夫特理工大学）；University College London（伦敦大学学院）
One-Shot Neural Architecture Search (NAS) is a promising method to significantly reduce search time without any separate training. It can be treated as a Network Compression problem on the architecture parameters from an over-parameterized network. However, there are two issues associated with most one-shot NAS methods. First, dependencies between a node and its predecessors and successors are often disregarded which result in improper treatment over zero operations. Second, architecture parameters pruning based on their magnitude is questionable. In this paper, we employ the classic Bayesian …
When tuning the architecture and hyperparameters of large machine learning models for on-device deployment, it is desirable to understand the optimal trade-offs between on-device latency and model accuracy. In this work, we leverage recent methodological advances in Bayesian optimization over high-dimensional search spaces and multi-objective Bayesian optimization to efficiently explore these trade-offs for a production-scale on-device natural language understanding model at Facebook.
Inria（法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）；Université de Lorraine（洛林大学）
One of the most interesting features of Bayesian optimization for direct policy search is that it can leverage priors (e.g., from simulation or from previous tasks) to accelerate learning on a robot. In this paper, we are interested in situations for which several priors exist but we do not know in advance which one fits best the current situation. We tackle this problem by introducing a novel acquisition function, called Most Likely Expected Improvement (MLEI), that combines the likelihood of the priors and the expected improvement. We evaluate this new acquisition function on a transfer lear…
Siemens AG（西门子股份公司）；Technical University of Munich（慕尼黑工业大学）；University of Cambridge（剑桥大学）；Harvard University（哈佛大学）
We present an algorithm for model-based reinforcement learning that combines Bayesian neural networks (BNNs) with random roll-outs and stochastic optimization for policy learning. The BNNs are trained by minimizing $α$-divergences, allowing us to capture complicated statistical patterns in the transition dynamics, e.g. multi-modality and heteroskedasticity, which are usually missed by other common modeling approaches. We illustrate the performance of our method by solving a challenging benchmark where model-based approaches usually fail and by obtaining promising results in a real-world scenar…
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…
Bayesian optimization (BO) is a successful methodology to optimize black-box functions that are expensive to evaluate. While traditional methods optimize each black-box function in isolation, there has been recent interest in speeding up BO by transferring knowledge across multiple related black-box functions. In this work, we introduce a method to automatically design the BO search space by relying on evaluations of previous black-box functions. We depart from the common practice of defining a set of arbitrary search ranges a priori by considering search space geometries that are learned from…
Ensembling can improve the performance of Neural Networks, but existing approaches struggle when the architecture likelihood surface has dispersed, narrow peaks. Furthermore, existing methods construct equally weighted ensembles, and this is likely to be vulnerable to the failure modes of the weaker architectures. By viewing ensembling as approximately marginalising over architectures we construct ensembles using the tools of Bayesian Quadrature -- tools which are well suited to the exploration of likelihood surfaces with dispersed, narrow peaks. Additionally, the resulting ensembles consist o…
Applying Bayesian optimization in problems wherein the search space is unknown is challenging. To address this problem, we propose a systematic volume expansion strategy for the Bayesian optimization. We devise a strategy to guarantee that in iterative expansions of the search space, our method can find a point whose function value within epsilon of the objective function maximum. Without the need to specify any parameters, our algorithm automatically triggers a minimal expansion required iteratively. We derive analytic expressions for when to trigger the expansion and by how much to expand. W…
Bosch Center for Artificial Intelligence（博世人工智能中心）；ETH Zürich（苏黎世联邦理工学院）
We consider the problem of robust optimization within the well-established Bayesian optimization (BO) framework. While BO is intrinsically robust to noisy evaluations of the objective function, standard approaches do not consider the case of uncertainty about the input parameters. In this paper, we propose Noisy-Input Entropy Search (NES), a novel information-theoretic acquisition function that is designed to find robust optima for problems with both input and measurement noise. NES is based on the key insight that the robust objective in many cases can be modeled as a Gaussian process, howeve…
Bayesian optimization (BO) is a model-based approach to sequentially optimize expensive black-box functions, such as the validation error of a deep neural network with respect to its hyperparameters. In many real-world scenarios, the optimization is further subject to a priori unknown constraints. For example, training a deep network configuration may fail with an out-of-memory error when the model is too large. In this work, we focus on a general formulation of Gaussian process-based BO with continuous or binary constraints. We propose constrained Max-value Entropy Search (cMES), a novel info…
The statistical procedure used in the search for the Higgs boson is investigated in this paper. A Bayesian hierarchical model is proposed that uses the information provided by the theory in the analysis of the data generated by the particle detectors. In addition, we develop a Bayesian decision making procedure that combines the two steps of the current method (discovery and exclusion) into one and can be calibrated to satisfy frequency theory error rate requirements. .
Many real world scientific and industrial applications require optimizing multiple competing black-box objectives. When the objectives are expensive-to-evaluate, multi-objective Bayesian optimization (BO) is a popular approach because of its high sample efficiency. However, even with recent methodological advances, most existing multi-objective BO methods perform poorly on search spaces with more than a few dozen parameters and rely on global surrogate models that scale cubically with the number of observations. In this work we propose MORBO, a scalable method for multi-objective BO over high-…
Seoul National University（首尔国立大学）；SK Telecom Co., Ltd.（SK电讯株式会社）
The early pioneering Neural Architecture Search (NAS) works were multi-trial methods applicable to any general search space. The subsequent works took advantage of the early findings and developed weight-sharing methods that assume a structured search space typically with pre-fixed hyperparameters. Despite the amazing computational efficiency of the weight-sharing NAS algorithms, it is becoming apparent that multi-trial NAS algorithms are also needed for identifying very high-performance architectures, especially when exploring a general search space. In this work, we carefully review the late…
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 …
Finding an optimal parameter of a black-box function is important for searching stable material structures and finding optimal neural network structures, and Bayesian optimization algorithms are widely used for the purpose. However, most of existing Bayesian optimization algorithms can only handle vector data and cannot handle complex structured data. In this paper, we propose the topological Bayesian optimization, which can efficiently find an optimal solution from structured data using \emph{topological information}. More specifically, in order to apply Bayesian optimization to structured da…
Mean-field variational inference is a method for approximate Bayesian posterior inference. It approximates a full posterior distribution with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This requires the ability to integrate a sum of terms in the log joint likelihood using this factorized distribution. Often not all integrals are in closed form, which is typically handled by using a lower bound. We present an alternative algorithm based on stochastic optimization that allows for direct optimization of the variational lower bound. This method uses c…
Recently, neural architecture search (NAS) has been applied to automate the design of neural networks in real-world applications. A large number of algorithms have been developed to improve the search cost or the performance of the final selected architectures in NAS. Unfortunately, these NAS algorithms aim to select only one single well-performing architecture from their search spaces and thus have overlooked the capability of neural network ensemble (i.e., an ensemble of neural networks with diverse architectures) in achieving improved performance over a single final selected architecture. T…
We consider two active binary-classification problems with atypical objectives. In the first, active search, our goal is to actively uncover as many members of a given class as possible. In the second, active surveying, our goal is to actively query points to ultimately predict the proportion of a given class. Numerous real-world problems can be framed in these terms, and in either case typical model-based concerns such as generalization error are only of secondary importance. We approach these problems via Bayesian decision theory; after choosing natural utility functions, we derive the optim…
University of British Columbia（不列颠哥伦比亚大学）；University of Oxford（牛津大学）；University of Cambridge（剑桥大学）；Canadian Institute for Advanced Research（加拿大高等研究院）
Bayesian optimization is a sample-efficient method for black-box global optimization. How- ever, the performance of a Bayesian optimization method very much depends on its exploration strategy, i.e. the choice of acquisition function, and it is not clear a priori which choice will result in superior performance. While portfolio methods provide an effective, principled way of combining a collection of acquisition functions, they are often based on measures of past performance which can be misleading. To address this issue, we introduce the Entropy Search Portfolio (ESP): a novel approach to por…
Online field experiments are the gold-standard way of evaluating changes to real-world interactive machine learning systems. Yet our ability to explore complex, multi-dimensional policy spaces - such as those found in recommendation and ranking problems - is often constrained by the limited number of experiments that can be run simultaneously. To alleviate these constraints, we augment online experiments with an offline simulator and apply multi-task Bayesian optimization to tune live machine learning systems. We describe practical issues that arise in these types of applications, including bi…
ETH Zürich（苏黎世联邦理工学院）；University of Amsterdam（阿姆斯特丹大学）；Imperial College London（帝国理工学院）
We propose a novel Bayesian neural network architecture that can learn invariances from data alone by inferring a posterior distribution over different weight-sharing schemes. We show that our model outperforms other non-invariant architectures, when trained on datasets that contain specific invariances. The same holds true when no data augmentation is performed.
Applied Artificial Intelligence Institute (A2I2)（应用人工智能研究所（A2I2））；Deakin University（迪肯大学）
We propose an algorithm for Bayesian functional optimisation - that is, finding the function to optimise a process - guided by experimenter beliefs and intuitions regarding the expected characteristics (length-scale, smoothness, cyclicity etc.) of the optimal solution encoded into the covariance function of a Gaussian Process. Our algorithm generates a sequence of finite-dimensional random subspaces of functional space spanned by a set of draws from the experimenter's Gaussian Process. Standard Bayesian optimisation is applied on each subspace, and the best solution found used as a starting po…
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…
Computational models in fields such as computational neuroscience are often evaluated via stochastic simulation or numerical approximation. Fitting these models implies a difficult optimization problem over complex, possibly noisy parameter landscapes. Bayesian optimization (BO) has been successfully applied to solving expensive black-box problems in engineering and machine learning. Here we explore whether BO can be applied as a general tool for model fitting. First, we present a novel hybrid BO algorithm, Bayesian adaptive direct search (BADS), that achieves competitive performance with an a…
University of Amsterdam（阿姆斯特丹大学）；Canadian Institute for Advanced Research（加拿大高等研究院）
A major challenge in Bayesian Optimization is the boundary issue (Swersky, 2017) where an algorithm spends too many evaluations near the boundary of its search space. In this paper, we propose BOCK, Bayesian Optimization with Cylindrical Kernels, whose basic idea is to transform the ball geometry of the search space using a cylindrical transformation. Because of the transformed geometry, the Gaussian Process-based surrogate model spends less budget searching near the boundary, while concentrating its efforts relatively more near the center of the search region, where we expect the solution to …
Indian Institute of Technology Gandhinagar（甘地纳格尔印度理工学院）；Northeastern University（东北大学）；Pacific Northwest National Laboratory（太平洋西北国家实验室）
Advances in neural architecture search, as well as explainability and interpretability of connectionist architectures, have been reported in the recent literature. However, our understanding of how to design Bayesian Deep Learning (BDL) hyperparameters, specifically, the depth, width and ensemble size, for robust function mapping with uncertainty quantification, is still emerging. This paper attempts to further our understanding by mapping Bayesian connectionist representations to polynomials of different orders with varying noise types and ratios. We examine the noise-contaminated polynomials…
It is already reported in the literature that the performance of a machine learning algorithm is greatly impacted by performing proper Hyper-Parameter optimization. One of the ways to perform Hyper-Parameter optimization is by manual search but that is time consuming. Some of the common approaches for performing Hyper-Parameter optimization are Grid search Random search and Bayesian optimization using Hyperopt. In this paper, we propose a brand new approach for hyperparameter improvement i.e. Randomized-Hyperopt and then tune the hyperparameters of the XGBoost i.e. the Extreme Gradient Boostin…
National University of Singapore（新加坡国立大学）；MIT（麻省理工学院）
Although the existing max-value entropy search (MES) is based on the widely celebrated notion of mutual information, its empirical performance can suffer due to two misconceptions whose implications on the exploration-exploitation trade-off are investigated in this paper. These issues are essential in the development of future acquisition functions and the improvement of the existing ones as they encourage an accurate measure of the mutual information such as the rectified MES (RMES) acquisition function we develop in this work. Unlike the evaluation of MES, we derive a closed-form probability…
Many real-world problems can be phrased as a multi-objective optimization problem, where the goal is to identify the best set of compromises between the competing objectives. Multi-objective Bayesian optimization (BO) is a sample efficient strategy that can be deployed to solve these vector-valued optimization problems where access is limited to a number of noisy objective function evaluations. In this paper, we propose a novel information-theoretic acquisition function for BO called Joint Entropy Search (JES), which considers the joint information gain for the optimal set of inputs and output…
