When it comes to expensive black-box optimization problems, Bayesian Optimization (BO) is a well-known and powerful solution. Many real-world applications involve a large number of dimensions, hence scaling BO to high dimension is of much interest. However, state-of-the-art high-dimensional BO methods still suffer from the curse of dimensionality, highlighting the need for further improvements. In this work, we introduce BOIDS, a novel high-dimensional BO algorithm that guides optimization by a sequence of one-dimensional direction lines using a novel tailored line-based optimization procedure. To improve the efficiency, we also propose an adaptive selection technique to identify most optimal lines for each round of line-based optimization. Additionally, we incorporate a subspace embedding technique for better scaling to high-dimensional spaces. We further provide theoretical analysis of our proposed method to analyze its convergence property. Our extensive experimental results show that BOIDS outperforms state-of-the-art baselines on various synthetic and real-world benchmark problems.

High-dimensional Bayesian Optimization (BO) has attracted significant attention in recent research. However, existing methods have mainly focused on optimizing in continuous domains, while combinatorial (ordinal and categorical) and mixed domains still remain challenging. In this paper, we first propose MOCA-HESP, a novel high-dimensional BO method for combinatorial and mixed variables. The key idea is to leverage the hyper-ellipsoid space partitioning (HESP) technique with different categorical encoders to work with high-dimensional, combinatorial and mixed spaces, while adaptively selecting the optimal encoders for HESP using a multi-armed bandit technique. Our method, MOCA-HESP, is designed as a meta-algorithm such that it can incorporate other combinatorial and mixed BO optimizers to further enhance the optimizers’ performance. Finally, we develop three practical BO methods by integrating MOCA-HESP with state-of-the-art BO optimizers for combinatorial and mixed variables: standard BO, CASMOPOLITAN, and Bounce. Our experimental results on various synthetic and real-world benchmarks show that our methods outperform existing baselines. Our code implementation can be found at https://github.com/LamNgo1/moca-hesp.

Bayesian Optimization (BO) is a powerful tool for optimizing expensive black-box objective functions. While extensive research has been conducted on the single-objective optimization problem, the multi-objective optimization problem remains challenging. In this paper, we propose MOBO-OSD, a multi-objective Bayesian Optimization algorithm designed to generate a diverse set of Pareto optimal solutions by solving multiple constrained optimization problems, referred to as MOBO-OSD subproblems, along orthogonal search directions (OSDs) defined with respect to an approximated convex hull of individual objective minima. By employing a well-distributed set of OSDs, MOBO-OSD ensures broad coverage of the objective space, enhancing both solution diversity and hypervolume performance. To further improve the density of the set of the Pareto optimal candidate solutions without requiring an excessive number of subproblems, we leverage a Pareto Front Estimation technique to generate additional solutions in the neighborhood of existing solutions. Additionally, MOBO-OSD supports batch optimization, enabling parallel function evaluations to accelerate the optimization process when resources are available. Through extensive experiments and analysis on a variety of synthetic and real-world benchmark functions with two to six objectives, we demonstrate that MOBO-OSD consistently outperform the state-of-the-art algorithms.

Microservice architecture has become a popular architecture adopted by many cloud applications. However, identifying the root cause of a failure in microservice systems is still a challenging and time-consuming task. In recent years, researchers have introduced various causal inference-based root cause analysis methods to assist engineers in identifying the root causes. To gain a better understanding of the current status of causal inference-based root cause analysis techniques for microservice systems, we conduct a comprehensive evaluation of nine causal discovery methods and twenty-one root cause analysis methods. Our evaluation aims to understand both the effectiveness and efficiency of causal inference-based root cause analysis methods, as well as other factors that affect their performance. Our experimental results and analyses indicate that no method stands out in all situations; each method tends to either fall short in effectiveness, efficiency, or shows sensitivity to specific parameters. Notably, the performance of root cause analysis methods on synthetic datasets may not accurately reflect their performance in real systems. Indeed, there is still a large room for further improvement. Furthermore, we also suggest possible future work based on our findings.

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) explicit LSE problem where the threshold level is a fixed user-specified value, and, (2) 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 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 methods can achieve better results compared to existing state-of-the-art approaches.

This work proposes a Bayesian optimisation with Gaussian Process approach to learn decision maker (DM) preferences in the attribute search space of a multi-objective optimisation problem (MOP). The DM is consulted periodically during optimisation of the problem and asked to provide their preference over a series of pairwise comparisons of candidate solutions. After each consultation, the most preferred solution is used as the reference point in an appropriate multiobjective optimisation evolutionary algorithm (MOEA). The rationale for using Bayesian optimisation is to identify the most preferred location in the decision search space with the least number of DM queries, thereby minimising DM cognitive burden and fatigue. This enables non-expert DMs to be involved in the optimisation process and make more informed decisions. We further reduce the number of preference queries required, by progressively redefining the Bayesian search space to reflect the MOEA's decision bounds as it converges toward the Pareto Front. We demonstrate how this approach can locate a reference point close to an unknown preferred location on the Pareto Front, of both benchmark and real-world problems with relatively few pairwise comparisons.

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.

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 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 \emph{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.

Many software systems provide users with a set of configuration options and different configurations may lead to different runtime performance of the system. As the combination of configurations could be exponential, it is difficult to exhaustively deploy and measure system performance under all possible configurations. Recently, several learning methods have been proposed to build a performance prediction model based on performance data collected from a small sample of configurations, and then use the model to predict system performance under a new configuration. In this paper, we propose a novel approach to model highly configurable software system using a deep feedforward neural network (FNN) combined with a sparsity regularization technique, e.g. the L1 regularization. Besides, we also design a practical search strategy for automatically tuning the network hyperparameters efficiently. Our method, called DeepPerf, can predict performance values of highly configurable software systems with binary and/or numeric configuration options at much higher prediction accuracy with less training data than the state-of-the art approaches. Experimental results on eleven public real-world datasets confirm the effectiveness of our approach.

Many software systems are highly configurable, which provide a large number of configuration options for users to choose from. During the maintenance and operation of these configurable systems, it is important to estimate the system performance under any specific configurations and understand the performance-influencing configuration options. However, it is often not feasible to measure the system performance under all the possible configurations as the combination of configurations could be exponential. In this paper, we propose PerLasso, a performance modeling and prediction method based on Fourier Learning and Lasso (Least absolute shrinkage and selection operator) regression techniques. Using a small sample of measured performance values of a configurable system, PerLasso produces a performance-influence model, which can 1) predict system performance under a new configuration; 2) explain the influence of the individual features and their interactions on the software performance. Besides, to reduce the number of Fourier coefficients to be estimated for large-scale systems, we also design a novel dimension reduction algorithm. Our experimental results on four synthetic and six real-world datasets confirm the effectiveness of our approach. Compared to the existing performance-influence models, our models have higher or comparable prediction accuracy.

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.