Black-box optimization is one of the vital tasks in machine learning, since it approximates real-world conditions, in that we do not always know all the properties of a given system, up to knowing almost nothing but the results. This paper describes our approach to solving the black-box optimization challenge at NeurIPS 2020 through learning search space partition for local Bayesian optimization. We describe the task of the challenge as well as our algorithm for low budget optimization that we named \texttt{SPBOpt}. We optimize the hyper-parameters of our algorithm for the competition finals using multi-task Bayesian optimization on results from the first two evaluation settings. Our approach has ranked third in the competition finals.
Challenging optimization problems, which elude acceptable solution via conventional calculus methods, arise commonly in different areas of industrial design and practice. Hard optimization problems are those who manifest the following behavior: a) high number of independent input variables; b) very complex or irregular multi-modal fitness; c) computational expensive fitness evaluation. This paper will focus on some theoretical issues that have strong implications for practice. I will stress how an interpretation of the No Free Lunch theorem leads naturally to a general Bayesian optimization fr…
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Bosch Center for AI（博世人工智能中心）；CMU（卡内基梅隆大学）
We focus on the problem of black-box adversarial attacks, where the aim is to generate adversarial examples using information limited to loss function evaluations of input-output pairs. We use Bayesian optimization~(BO) to specifically cater to scenarios involving low query budgets to develop query efficient adversarial attacks. We alleviate the issues surrounding BO in regards to optimizing high dimensional deep learning models by effective dimension upsampling techniques. Our proposed approach achieves performance comparable to the state of the art black-box adversarial attacks albeit with a…
In this work, we utilize a Trust Region based Derivative Free Optimization (DFO-TR) method to directly maximize the Area Under Receiver Operating Characteristic Curve (AUC), which is a nonsmooth, noisy function. We show that AUC is a smooth function, in expectation, if the distributions of the positive and negative data points obey a jointly normal distribution. The practical performance of this algorithm is compared to three prominent Bayesian optimization methods and random search. The presented numerical results show that DFO-TR surpasses Bayesian optimization and random search on various b…
Bayesian optimization (BO) is a framework for global optimization of expensive-to-evaluate objective functions. Classical BO methods assume that the objective function is a black box. However, internal information about objective function computation is often available. For example, when optimizing a manufacturing line's throughput with simulation, we observe the number of parts waiting at each workstation, in addition to the overall throughput. Recent BO methods leverage such internal information to dramatically improve performance. We call these "grey-box" BO methods because they treat objec…
We focus on the problem of adversarial attacks against models on discrete sequential data in the black-box setting where the attacker aims to craft adversarial examples with limited query access to the victim model. Existing black-box attacks, mostly based on greedy algorithms, find adversarial examples using pre-computed key positions to perturb, which severely limits the search space and might result in suboptimal solutions. To this end, we propose a query-efficient black-box attack using Bayesian optimization, which dynamically computes important positions using an automatic relevance deter…
Most existing black-box optimization methods assume that all variables in the system being optimized have equal cost and can change freely at each iteration. However, in many real world systems, inputs are passed through a sequence of different operations or modules, making variables in earlier stages of processing more costly to update. Such structure imposes a cost on switching variables in early parts of a data processing pipeline. In this work, we propose a new algorithm for switch cost-aware optimization called Lazy Modular Bayesian Optimization (LaMBO). This method efficiently identifies…
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…
Brown University（布朗大学）；Facebook AI Research（脸书人工智能研究院）
High dimensional black-box optimization has broad applications but remains a challenging problem to solve. Given a set of samples $\{\vx_i, y_i\}$, building a global model (like Bayesian Optimization (BO)) suffers from the curse of dimensionality in the high-dimensional search space, while a greedy search may lead to sub-optimality. By recursively splitting the search space into regions with high/low function values, recent works like LaNAS shows good performance in Neural Architecture Search (NAS), reducing the sample complexity empirically. In this paper, we coin LA-MCTS that extends LaNAS t…
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of California, Berkeley（加州大学伯克利分校）
Building surrogate models is one common approach when we attempt to learn unknown black-box functions. Bayesian optimization provides a framework which allows us to build surrogate models based on sequential samples drawn from the function and find the optimum. Tuning algorithmic parameters to optimize the performance of large, complicated "black-box" application codes is a specific important application, which aims at finding the optima of black-box functions. Within the Bayesian optimization framework, the Gaussian process model produces smooth or continuous sample paths. However, the black-…
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…
Southern University of Science and Technology（南方科技大学）
Black-box problems are common in real life like structural design, drug experiments, and machine learning. When optimizing black-box systems, decision-makers always consider multiple performances and give the final decision by comprehensive evaluations. Motivated by such practical needs, we focus on constrained black-box problems where the objective and constraints lack known special structure, and evaluations are expensive and even with noise. We develop a novel constrained Bayesian optimization approach based on the knowledge gradient method ($c-\rm{KG}$). A new acquisition function is propo…
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…
Efficient Black-box Adversarial Attacks via Bayesian Optimization Guided by a Function Prior
Tsinghua University（清华大学）；JQ Investments（JQ投资）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）；RealAI；Kaiyuan International Mathematical Sciences Institute（开源国际数学科学研究院）
ONERA（法国国家航空航天研究中心）；Université de Toulouse（图卢兹大学）；ISAE-SUPAERO（法国国立高等航空航天学院）
Bayesian optimization methods have been successfully applied to black box optimization problems that are expensive to evaluate. In this paper, we adapt the so-called super effcient global optimization algorithm to solve more accurately mixed constrained problems. The proposed approach handles constraints by means of upper trust bound, the latter encourages exploration of the feasible domain by combining the mean prediction and the associated uncertainty function given by the Gaussian processes. On top of that, a refinement procedure, based on a learning rate criterion, is introduced to enhance…
LIRIS, CNRS UMR 5205（里昂图像与信息系统实验室，法国国家科学研究中心 UMR 5205）；Ecole Centrale de Lyon（里昂中央理工学院）
We present a developmental framework based on a long-term memory and reasoning mechanisms (Vision Similarity and Bayesian Optimisation). This architecture allows a robot to optimize autonomously hyper-parameters that need to be tuned from any action and/or vision module, treated as a black-box. The learning can take advantage of past experiences (stored in the episodic and procedural memories) in order to warm-start the exploration using a set of hyper-parameters previously optimized from objects similar to the new unknown one (stored in a semantic memory). As example, the system has been used…
A new algorithm based on bayesian inference for learning local graph conductance based on Gaussian Process(GP) is given that uses advanced MCMC convergence ideas to create a scalable and fast algorithm for convergence to stationary distribution which is provided to learn the bahavior of conductance when traversing the indirected weighted graph. First metric embedding is used to represent the vertices of the graph. Then, uniform induced conductance is calculated for training points. Finally, in the learning step, a gaussian process is used to approximate the uniform induced conductance. MCMC is…
Recent advances in machine learning have led to increased deployment of black-box classifiers across a wide variety of applications. In many such situations there is a critical need to both reliably assess the performance of these pre-trained models and to perform this assessment in a label-efficient manner (given that labels may be scarce and costly to collect). In this paper, we introduce an active Bayesian approach for assessment of classifier performance to satisfy the desiderata of both reliability and label-efficiency. We begin by developing inference strategies to quantify uncertainty f…
We develop an optimization algorithm suitable for Bayesian learning in complex models. Our approach relies on natural gradient updates within a general black-box framework for efficient training with limited model-specific derivations. It applies within the class of exponential-family variational posterior distributions, for which we extensively discuss the Gaussian case for which the updates have a rather simple form. Our Quasi Black-box Variational Inference (QBVI) framework is readily applicable to a wide class of Bayesian inference problems and is of simple implementation as the updates of…
University of Bristol（布里斯托大学）；Spotify（声田）；University of Bath（巴斯大学）；University of Cambridge（剑桥大学）
We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor requires any problem-specific tuning, and is asymptotically exact for any density function with a bounded domain. The output is an approximation to the whole density function including the normalisation constant, via partitions organised in efficient data structures. Such approximations may be used for evidence estimation or fast posterior sampling, but also as b…
School of Mathematics and Statistics, University of New South Wales（新南威尔士大学数学与统计学院）；School of Computer Science, Fudan University（复旦大学计算机科学技术学院）；School of Computing and Information Systems, University of Melbourne（墨尔本大学计算与信息系统学院）
Bayesian nonparametric space partition (BNSP) models provide a variety of strategies for partitioning a $D$-dimensional space into a set of blocks. In this way, the data points lie in the same block would share certain kinds of homogeneity. BNSP models can be applied to various areas, such as regression/classification trees, random feature construction, relational modeling, etc. In this survey, we investigate the current progress of BNSP research through the following three perspectives: models, which review various strategies for generating the partitions in the space and discuss their theore…
Pennsylvania State University（宾夕法尼亚州立大学）；Applied Research Solutions（应用研究解决方案公司）；Air Force Research Lab（空军研究实验室）
Bayesian Neural Networks (BNNs), unlike Traditional Neural Networks (TNNs) are robust and adept at handling adversarial attacks by incorporating randomness. This randomness improves the estimation of uncertainty, a feature lacking in TNNs. Thus, we investigate the robustness of BNNs to white-box attacks using multiple Bayesian neural architectures. Furthermore, we create our BNN model, called BNN-DenseNet, by fusing Bayesian inference (i.e., variational Bayes) to the DenseNet architecture, and BDAV, by combining this intervention with adversarial training. Experiments are conducted on the CIFA…
Rochester Data Science Consortium（罗切斯特数据科学联盟）；University of Rochester（罗切斯特大学）
There are a large number of optimization problems in physical models where the relationships between model parameters and outputs are unknown or hard to track. These models are named as black-box models in general because they can only be viewed in terms of inputs and outputs, without knowledge of the internal workings. Optimizing the black-box model parameters has become increasingly expensive and time consuming as they have become more complex. Hence, developing effective and efficient black-box model optimization algorithms has become an important task. One powerful algorithm to solve such …
We develop a novel hybrid method for Bayesian network structure learning called partitioned hybrid greedy search (pHGS), composed of three distinct yet compatible new algorithms: Partitioned PC (pPC) accelerates skeleton learning via a divide-and-conquer strategy, $p$-value adjacency thresholding (PATH) effectively accomplishes parameter tuning with a single execution, and hybrid greedy initialization (HGI) maximally utilizes constraint-based information to obtain a high-scoring and well-performing initial graph for greedy search. We establish structure learning consistency of our algorithms i…
Council for Scientific and Industrial Research（科学与工业研究理事会）；University of Edinburgh（爱丁堡大学）；University of Pretoria（比勒陀利亚大学）
Saliency maps are often used in computer vision to provide intuitive interpretations of what input regions a model has used to produce a specific prediction. A number of approaches to saliency map generation are available, but most require access to model parameters. This work proposes an approach for saliency map generation for black-box models, where no access to model parameters is available, using a Bayesian optimisation sampling method. The approach aims to find the global salient image region responsible for a particular (black-box) model's prediction. This is achieved by a sampling-base…
Department of Statistics, University of California, Los Angeles（加利福尼亚大学洛杉矶分校统计学系）
Structure learning of Bayesian networks has always been a challenging problem. Nowadays, massive-size networks with thousands or more of nodes but fewer samples frequently appear in many areas. We develop a divide-and-conquer framework, called partition-estimation-fusion (PEF), for structure learning of such big networks. The proposed method first partitions nodes into clusters, then learns a subgraph on each cluster of nodes, and finally fuses all learned subgraphs into one Bayesian network. The PEF method is designed in a flexible way so that any structure learning method may be used in the …
The use of sophisticated machine learning models for critical decision making is faced with a challenge that these models are often applied as a "black-box". This has led to an increased interest in interpretable machine learning, where post hoc interpretation presents a useful mechanism for generating interpretations of complex learning models. In this paper, we propose a novel approach underpinned by an extended framework of Bayesian networks for generating post hoc interpretations of a black-box predictive model. The framework supports extracting a Bayesian network as an approximation of th…
Data-efficient learning algorithms are essential in many practical applications for which data collection is expensive, e.g., for the optimal deployment of wireless systems in unknown propagation scenarios. Meta-learning can address this problem by leveraging data from a set of related learning tasks, e.g., from similar deployment settings. In practice, one may have available only unlabeled data sets from the related tasks, requiring a costly labeling procedure to be carried out before use in meta-learning. For instance, one may know the possible positions of base stations in a given area, but…
Optimizing the Unknown: Black Box Bayesian Optimization with Energy-Based Model and Reinforcement Learning
University of California, Los Angeles（加州大学洛杉矶分校）；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）
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…
In many real-world problems, we want to infer some property of an expensive black-box function $f$, given a budget of $T$ function evaluations. One example is budget constrained global optimization of $f$, for which Bayesian optimization is a popular method. Other properties of interest include local optima, level sets, integrals, or graph-structured information induced by $f$. Often, we can find an algorithm $\mathcal{A}$ to compute the desired property, but it may require far more than $T$ queries to execute. Given such an $\mathcal{A}$, and a prior distribution over $f$, we refer to the pro…
Modelling human function learning has been the subject of in-tense research in cognitive sciences. The topic is relevant in black-box optimization where information about the objective and/or constraints is not available and must be learned through function evaluations. In this paper we focus on the relation between the behaviour of humans searching for the maximum and the probabilistic model used in Bayesian Optimization. As surrogate models of the unknown function both Gaussian Processes and Random Forest have been considered: the Bayesian learning paradigm is central in the development of a…
Bayesian optimal design of experiments (BODE) has been successful in acquiring information about a quantity of interest (QoI) which depends on a black-box function. BODE is characterized by sequentially querying the function at specific designs selected by an infill-sampling criterion. However, most current BODE methods operate in specific contexts like optimization, or learning a universal representation of the black-box function. The objective of this paper is to design a BODE for estimating the statistical expectation of a physical response surface. This QoI is omnipresent in uncertainty pr…
