We study the problem of performance optimization of closed-loop control systems with unmodeled dynamics. Bayesian optimization (BO) has been demonstrated to be effective for improving closed-loop performance by automatically tuning controller gains or reference setpoints in a model-free manner. However, BO methods have rarely been tested on dynamical systems with unmodeled constraints and time-varying ambient conditions. In this paper, we propose a violation-aware contextual BO algorithm (VACBO) that optimizes closed-loop performance while simultaneously learning constraint-feasible solutions under time-varying ambient conditions. Unlike classical constrained BO methods which allow unlimited constraint violations, or 'safe' BO algorithms that are conservative and try to operate with near-zero violations, we allow budgeted constraint violations to improve constraint learning and accelerate optimization. We demonstrate the effectiveness of our proposed VACBO method for energy minimization of industrial vapor compression systems under time-varying ambient temperature and humidity.
Batch Bayesian optimisation and Bayesian quadrature have been shown to be sample-efficient methods of performing optimisation and quadrature where expensive-to-evaluate objective functions can be queried in parallel. However, current methods do not scale to large batch sizes -- a frequent desideratum in practice (e.g. drug discovery or simulation-based inference). We present a novel algorithm, SOBER, which permits scalable and diversified batch global optimisation and quadrature with arbitrary acquisition functions and kernels over discrete and mixed spaces. The key to our approach is to reformulate batch selection for global optimisation as a quadrature problem, which relaxes acquisition function maximisation (non-convex) to kernel recombination (convex). Bridging global optimisation and quadrature can efficiently solve both tasks by balancing the merits of exploitative Bayesian optimisation and explorative Bayesian quadrature. We show that SOBER outperforms 11 competitive baselines on 12 synthetic and diverse real-world tasks.
Simulation-based falsification is a practical testing method to increase confidence that the system will meet safety requirements. Because full-fidelity simulations can be computationally demanding, we investigate the use of simulators with different levels of fidelity. As a first step, we express the overall safety specification in terms of environmental parameters and structure this safety specification as an optimization problem. We propose a multi-fidelity falsification framework using Bayesian optimization, which is able to determine at which level of fidelity we should conduct a safety evaluation in addition to finding possible instances from the environment that cause the system to fail. This method allows us to automatically switch between inexpensive, inaccurate information from a low-fidelity simulator and expensive, accurate information from a high-fidelity simulator in a cost-effective way. Our experiments on various environments in simulation demonstrate that multi-fidelity Bayesian optimization has falsification performance comparable to single-fidelity Bayesian optimization but with much lower cost.
Tensor robust principal component analysis (RPCA), which seeks to separate a low-rank tensor from its sparse corruptions, has been crucial in data science and machine learning where tensor structures are becoming more prevalent. While powerful, existing tensor RPCA algorithms can be difficult to use in practice, as their performance can be sensitive to the choice of additional hyperparameters, which are not straightforward to tune. In this paper, we describe a fast and simple self-supervised model for tensor RPCA using deep unfolding by only learning four hyperparameters. Despite its simplicity, our model expunges the need for ground truth labels while maintaining competitive or even greater performance compared to supervised deep unfolding. Furthermore, our model is capable of operating in extreme data-starved scenarios. We demonstrate these claims on a mix of synthetic data and real-world tasks, comparing performance against previously studied supervised deep unfolding methods and Bayesian optimization baselines.
Bayesian optimization (BO), while proved highly effective for many black-box function optimization tasks, requires practitioners to carefully select priors that well model their functions of interest. Rather than specifying by hand, researchers have investigated transfer learning based methods to automatically learn the priors, e.g. multi-task BO (Swersky et al., 2013), few-shot BO (Wistuba and Grabocka, 2021) and HyperBO (Wang et al., 2022). However, those prior learning methods typically assume that the input domains are the same for all tasks, weakening their ability to use observations on functions with different domains or generalize the learned priors to BO on different search spaces. In this work, we present HyperBO+: a pre-training approach for hierarchical Gaussian processes that enables the same prior to work universally for Bayesian optimization on functions with different domains. We propose a two-step pre-training method and analyze its appealing asymptotic properties and benefits to BO both theoretically and empirically. On real-world hyperparameter tuning tasks that involve multiple search spaces, we demonstrate that HyperBO+ is able to generalize to unseen search spaces and achieves lower regrets than competitive baselines.
Deep learning models that leverage large datasets are often the state of the art for modelling molecular properties. When the datasets are smaller (< 2000 molecules), it is not clear that deep learning approaches are the right modelling tool. In this work we perform an extensive study of the calibration and generalizability of probabilistic machine learning models on small chemical datasets. Using different molecular representations and models, we analyse the quality of their predictions and uncertainties in a variety of tasks (binary, regression) and datasets. We also introduce two simulated experiments that evaluate their performance: (1) Bayesian optimization guided molecular design, (2) inference on out-of-distribution data via ablated cluster splits. We offer practical insights into model and feature choice for modelling small chemical datasets, a common scenario in new chemical experiments. We have packaged our analysis into the DIONYSUS repository, which is open sourced to aid in reproducibility and extension to new datasets.
Hyperparameter optimization (HPO) is crucial for strong performance of deep learning algorithms and real-world applications often impose some constraints, such as memory usage, or latency on top of the performance requirement. In this work, we propose constrained TPE (c-TPE), an extension of the widely-used versatile Bayesian optimization method, tree-structured Parzen estimator (TPE), to handle these constraints. Our proposed extension goes beyond a simple combination of an existing acquisition function and the original TPE, and instead includes modifications that address issues that cause poor performance. We thoroughly analyze these modifications both empirically and theoretically, providing insights into how they effectively overcome these challenges. In the experiments, we demonstrate that c-TPE exhibits the best average rank performance among existing methods with statistical significance on 81 expensive HPO with inequality constraints. Due to the lack of baselines, we only discuss the applicability of our method to hard-constrained optimization in Appendix D.
How should we intervene on an unknown structural equation model to maximize a downstream variable of interest? This setting, also known as causal Bayesian optimization (CBO), has important applications in medicine, ecology, and manufacturing. Standard Bayesian optimization algorithms fail to effectively leverage the underlying causal structure. Existing CBO approaches assume noiseless measurements and do not come with guarantees. We propose the model-based causal Bayesian optimization algorithm (MCBO) that learns a full system model instead of only modeling intervention-reward pairs. MCBO propagates epistemic uncertainty about the causal mechanisms through the graph and trades off exploration and exploitation via the optimism principle. We bound its cumulative regret, and obtain the first non-asymptotic bounds for CBO. Unlike in standard Bayesian optimization, our acquisition function cannot be evaluated in closed form, so we show how the reparameterization trick can be used to apply gradient-based optimizers. The resulting practical implementation of MCBO compares favorably with state-of-the-art approaches empirically.
Bayesian optimization (BO) algorithms form a class of surrogate-based heuristics, aimed at efficiently computing high-quality solutions for numerical black-box optimization problems. The BO pipeline is highly modular, with different design choices for the initial sampling strategy, the surrogate model, the acquisition function (AF), the solver used to optimize the AF, etc. We demonstrate in this work that a dynamic selection of the AF can benefit the BO design. More precisely, we show that already a na\"ive random forest regression model, built on top of exploratory landscape analysis features that are computed from the initial design points, suffices to recommend AFs that outperform any static choice, when considering performance over the classic BBOB benchmark suite for derivative-free numerical optimization methods on the COCO platform. Our work hence paves a way towards AutoML-assisted, on-the-fly BO designs that adjust their behavior on a run-by-run basis.
Bayesian Optimization is a useful tool for experiment design. Unfortunately, the classical, sequential setting of Bayesian Optimization does not translate well into laboratory experiments, for instance battery design, where measurements may come from different sources and their evaluations may require significant waiting times. Multi-fidelity Bayesian Optimization addresses the setting with measurements from different sources. Asynchronous batch Bayesian Optimization provides a framework to select new experiments before the results of the prior experiments are revealed. This paper proposes an algorithm combining multi-fidelity and asynchronous batch methods. We empirically study the algorithm behavior, and show it can outperform single-fidelity batch methods and multi-fidelity sequential methods. As an application, we consider designing electrode materials for optimal performance in pouch cells using experiments with coin cells to approximate battery performance.
Bayesian optimization (BO) is increasingly employed in critical applications such as materials design and drug discovery. An increasingly popular strategy in BO is to forgo the sole reliance on high-fidelity data and instead use an ensemble of information sources which provide inexpensive low-fidelity data. The overall premise of this strategy is to reduce the overall sampling costs by querying inexpensive low-fidelity sources whose data are correlated with high-fidelity samples. Here, we propose a multi-fidelity cost-aware BO framework that dramatically outperforms the state-of-the-art technologies in terms of efficiency, consistency, and robustness. We demonstrate the advantages of our framework on analytic and engineering problems and argue that these benefits stem from our two main contributions: (1) we develop a novel acquisition function for multi-fidelity cost-aware BO that safeguards the convergence against the biases of low-fidelity data, and (2) we tailor a newly developed emulator for multi-fidelity BO which enables us to not only simultaneously learn from an ensemble of multi-fidelity datasets, but also identify the severely biased low-fidelity sources that should be excluded from BO.
Bayesian Optimization (BO) is a powerful, sample-efficient technique to optimize expensive-to-evaluate functions. Each of the BO components, such as the surrogate model, the acquisition function (AF), or the initial design, is subject to a wide range of design choices. Selecting the right components for a given optimization task is a challenging task, which can have significant impact on the quality of the obtained results. In this work, we initiate the analysis of which AF to favor for which optimization scenarios. To this end, we benchmark SMAC3 using Expected Improvement (EI) and Probability of Improvement (PI) as acquisition functions on the 24 BBOB functions of the COCO environment. We compare their results with those of schedules switching between AFs. One schedule aims to use EI's explorative behavior in the early optimization steps, and then switches to PI for a better exploitation in the final steps. We also compare this to a random schedule and round-robin selection of EI and PI. We observe that dynamic schedules oftentimes outperform any single static one. Our results suggest that a schedule that allocates the first 25 % of the optimization budget to EI and the last 75 % to PI is a reliable default. However, we also observe considerable performance differences for the 24 functions, suggesting that a per-instance allocation, possibly learned on the fly, could offer significant improvement over the state-of-the-art BO designs.
The optimization of high-dimensional black-box functions is a challenging problem. When a low-dimensional linear embedding structure can be assumed, existing Bayesian optimization (BO) methods often transform the original problem into optimization in a low-dimensional space. They exploit the low-dimensional structure and reduce the computational burden. However, we reveal that this approach could be limited or inefficient in exploring the high-dimensional space mainly due to the biased reconstruction of the high-dimensional queries from the low-dimensional queries. In this paper, we investigate a simple alternative approach: tackling the problem in the original high-dimensional space using the information from the learned low-dimensional structure. We provide a theoretical analysis of the exploration ability. Furthermore, we show that our method is applicable to batch optimization problems with thousands of dimensions without any computational difficulty. We demonstrate the effectiveness of our method on high-dimensional benchmarks and a real-world function.
The Adaptive Large Neighborhood Search (ALNS) algorithm has shown considerable success in solving combinatorial optimization problems (COPs). Nonetheless, the performance of ALNS relies on the proper configuration of its selection and acceptance parameters, which is known to be a complex and resource-intensive task. To address this, we introduce a Deep Reinforcement Learning (DRL) based approach called DR-ALNS that selects operators, adjusts parameters, and controls the acceptance criterion throughout the search. The proposed method aims to learn, based on the state of the search, to configure ALNS for the next iteration to yield more effective solutions for the given optimization problem. We evaluate the proposed method on an orienteering problem with stochastic weights and time windows, as presented in an IJCAI competition. The results show that our approach outperforms vanilla ALNS, ALNS tuned with Bayesian optimization, and two state-of-the-art DRL approaches that were the winning methods of the competition, achieving this with significantly fewer training observations. Furthermore, we demonstrate several good properties of the proposed DR-ALNS method: it is easily adapted to solve different routing problems, its learned policies perform consistently well across various instance sizes, and these policies can be directly applied to different problem variants.
Network slicing achieves cost-efficient slice customization to support heterogeneous applications and services. Configuring cross-domain resources to end-to-end slices based on service-level agreements, however, is challenging, due to the complicated underlying correlations and the simulation-to-reality discrepancy between simulators and real networks. In this paper, we propose Atlas, an online network slicing system, which automates the service configuration of slices via safe and sample-efficient learn-to-configure approaches in three interrelated stages. First, we design a learning-based simulator to reduce the sim-to-real discrepancy, which is accomplished by a new parameter searching method based on Bayesian optimization. Second, we offline train the policy in the augmented simulator via a novel offline algorithm with a Bayesian neural network and parallel Thompson sampling. Third, we online learn the policy in real networks with a novel online algorithm with safe exploration and Gaussian process regression. We implement Atlas on an end-to-end network prototype based on OpenAirInterface RAN, OpenDayLight SDN transport, OpenAir-CN core network, and Docker-based edge server. Experimental results show that, compared to state-of-the-art solutions, Atlas achieves 63.9% and 85.7% regret reduction on resource usage and slice quality of experience during the online learning stage, respectively.
Bayesian optimization (BO) is a powerful framework for optimizing black-box, expensive-to-evaluate functions. Over the past decade, many algorithms have been proposed to integrate cheaper, lower-fidelity approximations of the objective function into the optimization process, with the goal of converging towards the global optimum at a reduced cost. This task is generally referred to as multi-fidelity Bayesian optimization (MFBO). However, MFBO algorithms can lead to higher optimization costs than their vanilla BO counterparts, especially when the low-fidelity sources are poor approximations of the objective function, therefore defeating their purpose. To address this issue, we propose rMFBO (robust MFBO), a methodology to make any GP-based MFBO scheme robust to the addition of unreliable information sources. rMFBO comes with a theoretical guarantee that its performance can be bound to its vanilla BO analog, with high controllable probability. We demonstrate the effectiveness of the proposed methodology on a number of numerical benchmarks, outperforming earlier MFBO methods on unreliable sources. We expect rMFBO to be particularly useful to reliably include human experts with varying knowledge within BO processes.
Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e. objective function queries) with maximal expected utility with respect to the posterior distribution of a Bayesian model, which quantifies reducible, epistemic uncertainty about query outcomes. In practice, subjectively implausible outcomes can occur regularly for two reasons: 1) model misspecification and 2) covariate shift. Conformal prediction is an uncertainty quantification method with coverage guarantees even for misspecified models and a simple mechanism to correct for covariate shift. We propose conformal Bayesian optimization, which directs queries towards regions of search space where the model predictions have guaranteed validity, and investigate its behavior on a suite of black-box optimization tasks and tabular ranking tasks. In many cases we find that query coverage can be significantly improved without harming sample-efficiency.
Local optimization presents a promising approach to expensive, high-dimensional black-box optimization by sidestepping the need to globally explore the search space. For objective functions whose gradient cannot be evaluated directly, Bayesian optimization offers one solution -- we construct a probabilistic model of the objective, design a policy to learn about the gradient at the current location, and use the resulting information to navigate the objective landscape. Previous work has realized this scheme by minimizing the variance in the estimate of the gradient, then moving in the direction of the expected gradient. In this paper, we re-examine and refine this approach. We demonstrate that, surprisingly, the expected value of the gradient is not always the direction maximizing the probability of descent, and in fact, these directions may be nearly orthogonal. This observation then inspires an elegant optimization scheme seeking to maximize the probability of descent while moving in the direction of most-probable descent. Experiments on both synthetic and real-world objectives show that our method outperforms previous realizations of this optimization scheme and is competitive against other, significantly more complicated baselines.
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 distance between GP's directly in function space to construct a kernel-kernel. We present an alternative approach by defining a kernel-kernel over the symbolic representation of the statistical hypothesis that is associated with a kernel. We empirically show that this leads to a computationally more efficient way of searching through a discrete kernel space.
Bayesian optimization (BO) is a popular approach for sample-efficient optimization of black-box objective functions. While BO has been successfully applied to a wide range of scientific applications, traditional approaches to single-objective BO only seek to find a single best solution. This can be a significant limitation in situations where solutions may later turn out to be intractable. For example, a designed molecule may turn out to violate constraints that can only be reasonably evaluated after the optimization process has concluded. To address this issue, we propose Rank-Ordered Bayesian Optimization with Trust-regions (ROBOT) which aims to find a portfolio of high-performing solutions that are diverse according to a user-specified diversity metric. We evaluate ROBOT on several real-world applications and show that it can discover large sets of high-performing diverse solutions while requiring few additional function evaluations compared to finding a single best solution.