High-dimensional Bayesian Optimization via Covariance Matrix Adaptation Strategy

Bayesian Optimization (BO) is an effective method for finding the global optimum of expensive black-box functions. However, it is well known that applying BO to high-dimensional optimization problems is challenging. To address this issue, a promising solution is to use a local search strategy that partitions the search domain into local regions with high likelihood of containing the global optimum, and then use BO to optimize the objective function within these regions. In this paper, we propose a novel technique for defining the local regions using the Covariance Matrix Adaptation (CMA) strategy. Specifically, we use CMA to learn a search distribution that can estimate the probabilities of data points being the global optimum of the objective function. Based on this search distribution, we then define the local regions consisting of data points with high probabilities of being the global optimum. Our approach serves as a meta-algorithm as it can incorporate existing black-box BO optimizers, such as BO, TuRBO, and BAxUS, to find the global optimum of the objective function within our derived local regions. We evaluate our proposed method on various benchmark synthetic and real-world problems. The results demonstrate that our method outperforms existing state-of-the-art techniques.

Provably Efficient Bayesian Optimization with Unbiased Gaussian Process Hyperparameter Estimation

Gaussian process (GP) based Bayesian optimization (BO) is a powerful method for optimizing black-box functions efficiently. The practical performance and theoretical guarantees associated with this approach depend on having the correct GP hyperparameter values, which are usually unknown in advance and need to be estimated from the observed data. However, in practice, these estimations could be incorrect due to biased data sampling strategies commonly used in BO. This can lead to degraded performance and break the sub-linear global convergence guarantee of BO. To address this issue, we propose a new BO method that can sub-linearly converge to the global optimum of the objective function even when the true GP hyperparameters are unknown in advance and need to be estimated from the observed data. Our method uses a multi-armed bandit technique (EXP3) to add random data points to the BO process, and employs a novel training loss function for the GP hyperparameter estimation process that ensures unbiased estimation from the observed data. We further provide theoretical analysis of our proposed method. Finally, we demonstrate empirically that our method outperforms existing approaches on various synthetic and real-world problems.

Uncertainty-Aware Performance Prediction for Highly Configurable Software Systems via Bayesian Neural Networks

Configurable software systems are employed in many important application domains. Understanding the performance of the systems under all configurations is critical to prevent potential performance issues caused by misconfiguration. However, as the number of configurations can be prohibitively large, it is not possible to measure the system performance under all configurations. Thus, a common approach is to build a prediction model from a limited measurement data to predict the performance of all configurations as scalar values. However, it has been pointed out that there are different sources of uncertainty coming from the data collection or the modeling process, which can make the scalar predictions not certainly accurate. To address this problem, we propose a Bayesian deep learning based method, namely BDLPerf, that can incorporate uncertainty into the prediction model. BDLPerf can provide both scalar predictions for configurations' performance and the corresponding confidence intervals of these scalar predictions. We also develop a novel uncertainty calibration technique to ensure the reliability of the confidence intervals generated by a Bayesian prediction model. Finally, we suggest an efficient hyperparameter tuning technique so as to train the prediction model within a reasonable amount of time whilst achieving high accuracy. Our experimental results on 10 real-world systems show that BDLPerf achieves higher accuracy than existing approaches, in both scalar performance prediction and confidence interval estimation.

An Efficient Framework for Monitoring Subgroup Performance of Machine Learning Systems

Monitoring machine learning systems post deployment is critical to ensure the reliability of the systems. Particularly importance is the problem of monitoring the performance of machine learning systems across all the data subgroups (subpopulations). In practice, this process could be prohibitively expensive as the number of data subgroups grows exponentially with the number of input features, and the process of labelling data to evaluate each subgroup's performance is costly. In this paper, we propose an efficient framework for monitoring subgroup performance of machine learning systems. Specifically, we aim to find the data subgroup with the worst performance using a limited number of labeled data. We mathematically formulate this problem as an optimization problem with an expensive black-box objective function, and then suggest to use Bayesian optimization to solve this problem. Our experimental results on various real-world datasets and machine learning systems show that our proposed framework can retrieve the worst-performing data subgroup effectively and efficiently.

ALT-MAS: A Data-Efficient Framework for Active Testing of Machine Learning Algorithms

Machine learning models are being used extensively in many important areas, but there is no guarantee a model will always perform well or as its developers intended. Understanding the correctness of a model is crucial to prevent potential failures that may have significant detrimental impact in critical application areas. In this paper, we propose a novel framework to efficiently test a machine learning model using only a small amount of labeled test data. The idea is to estimate the metrics of interest for a model-under-test using Bayesian neural network (BNN). We develop a novel data augmentation method helping to train the BNN to achieve high accuracy. We also devise a theoretic information based sampling strategy to sample data points so as to achieve accurate estimations for the metrics of interest. Finally, we conduct an extensive set of experiments to test various machine learning models for different types of metrics. Our experiments show that the metrics estimations by our method are significantly better than existing baselines.

Think Global and Act Local: Bayesian Optimisation over High-Dimensional Categorical and Mixed Search Spaces

High-dimensional black-box optimisation remains an important yet notoriously challenging problem. Despite the success of Bayesian optimisation methods on continuous domains, domains that are categorical, or that mix continuous and categorical variables, remain challenging. We propose a novel solution -- we combine local optimisation with a tailored kernel design, effectively handling high-dimensional categorical and mixed search spaces, whilst retaining sample efficiency. We further derive convergence guarantee for the proposed approach. Finally, we demonstrate empirically that our method outperforms the current baselines on a variety of synthetic and real-world tasks in terms of performance, computational costs, or both.

High Dimensional Level Set Estimation with Bayesian Neural Network

Level Set Estimation (LSE) is an important problem with applications in various fields such as material design, biotechnology, machine operational testing, etc. Existing techniques suffer from the scalability issue, that is, these methods do not work well with high dimensional inputs. This paper proposes novel methods to solve the high dimensional LSE problems using Bayesian Neural Networks. In particular, we consider two types of LSE problems: (1) \textit{explicit} LSE problem where the threshold level is a fixed user-specified value, and, (2) \textit{implicit} LSE problem where the threshold level is defined as a percentage of the (unknown) maximum of the objective function. For each problem, we derive the corresponding theoretic information based acquisition function to sample the data points so as to maximally increase the level set accuracy. Furthermore, we also analyse the theoretical time complexity of our proposed acquisition functions, and suggest a practical methodology to efficiently tune the network hyper-parameters to achieve high model accuracy. Numerical experiments on both synthetic and real-world datasets show that our proposed method can achieve better results compared to existing state-of-the-art approaches.

Sub-linear Regret Bounds for Bayesian Optimisation in Unknown Search Spaces

Bayesian optimisation is a popular method for efficient optimisation of expensive black-box functions. Traditionally, BO assumes that the search space is known. However, in many problems, this assumption does not hold. To this end, we propose a novel BO algorithm which expands (and shifts) the search space over iterations based on controlling the expansion rate thought a hyperharmonic series. Further, we propose another variant of our algorithm that scales to high dimensions. We show theoretically that for both our algorithms, the cumulative regret grows at sub-linear rates. Our experiments with synthetic and real-world optimisation tasks demonstrate the superiority of our algorithms over the current state-of-the-art methods for Bayesian optimisation in unknown search space.

Distributionally Robust Bayesian Quadrature Optimization

Bayesian quadrature optimization (BQO) maximizes the expectation of an expensive black-box integrand taken over a known probability distribution. In this work, we study BQO under distributional uncertainty in which the underlying probability distribution is unknown except for a limited set of its i.i.d. samples. A standard BQO approach maximizes the Monte Carlo estimate of the true expected objective given the fixed sample set. Though Monte Carlo estimate is unbiased, it has high variance given a small set of samples; thus can result in a spurious objective function. We adopt the distributionally robust optimization perspective to this problem by maximizing the expected objective under the most adversarial distribution. In particular, we propose a novel posterior sampling based algorithm, namely distributionally robust BQO (DRBQO) for this purpose. We demonstrate the empirical effectiveness of our proposed framework in synthetic and real-world problems, and characterize its theoretical convergence via Bayesian regret.

Bayesian Optimization with Unknown Search Space

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. We also provide theoretical analysis to show that our method achieves epsilon-accuracy after a finite number of iterations. We demonstrate our method on both benchmark test functions and machine learning hyper-parameter tuning tasks and demonstrate that our method outperforms baselines.