This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical GP-UCB algorithm, but the additional random exploration step accelerates their convergence, nearly achieving the optimal convergence rate. Furthermore, to facilitate Bayesian inference with an intractable likelihood, we propose to utilize optimization iterates for maximum a posteriori estimation to build a Gaussian process surrogate model for the unnormalized log-posterior density. We provide bounds for the Hellinger distance between the true and the approximate posterior distributions in terms of the number of design points. We demonstrate the effectiveness of our Bayesian optimization algorithms in non-convex benchmark objective functions, in a machine learning hyperparameter tuning problem, and in a black-box engineering design problem. The effectiveness of our posterior approximation approach is demonstrated in two Bayesian inference problems for parameters of dynamical systems.
Bayesian optimization (BO) is a powerful technology for optimizing noisy expensive-to-evaluate black-box functions, with a broad range of real-world applications in science, engineering, economics, manufacturing, and beyond. In this paper, we provide an overview of recent developments, challenges, and opportunities in BO for design of next-generation process systems. After describing several motivating applications, we discuss how advanced BO methods have been developed to more efficiently tackle important problems in these applications. We conclude the paper with a summary of challenges and opportunities related to improving the quality of the probabilistic model, the choice of internal optimization procedure used to select the next sample point, and the exploitation of problem structure to improve sample efficiency.
Bayesian optimization (BO) has established itself as a leading strategy for efficiently optimizing expensive-to-evaluate functions. Existing BO methods mostly rely on Gaussian process (GP) surrogate models and are not applicable to (doubly-stochastic) Gaussian Cox processes, where the observation process is modulated by a latent intensity function modeled as a GP. In this paper, we propose a novel maximum a posteriori inference of Gaussian Cox processes. It leverages the Laplace approximation and change of kernel technique to transform the problem into a new reproducing kernel Hilbert space, where it becomes more tractable computationally. It enables us to obtain both a functional posterior of the latent intensity function and the covariance of the posterior, thus extending existing works that often focus on specific link functions or estimating the posterior mean. Using the result, we propose a BO framework based on the Gaussian Cox process model and further develop a Nystr\"om approximation for efficient computation. Extensive evaluations on various synthetic and real-world datasets demonstrate significant improvement over state-of-the-art inference solutions for Gaussian Cox processes, as well as effective BO with a wide range of acquisition functions designed through the underlying Gaussian Cox process model.
There is great interest in minimizing the impact forces of reluctance actuators during commutations, in order to reduce contact bouncing, acoustic noise and mechanical wear. In this regard, a run-to-run control algorithm is proposed to decrease the contact velocity, by exploiting the repetitive operations of these devices. The complete control is presented, with special focus on the optimization method and the input definition. The search method is based on Bayesian optimization, and several additions are introduced for its application in run-to-run control, e.g. the removal of stored points and the definition of a new acquisition function. Additionally, methods for the input parametrization and dimension reduction are presented. For analysis, Monte Carlo simulations are performed using a dynamic model of a commercial solenoid valve, comparing the proposed search method with two alternatives. Furthermore, the control strategy is validated through experimental testing, using several devices from the same ensemble of solenoid valves.
Manual parameter tuning of cyber-physical systems is a common practice, but it is labor-intensive. Bayesian Optimization (BO) offers an automated alternative, yet its black-box nature reduces trust and limits human-BO collaborative system tuning. Experts struggle to interpret BO recommendations due to the lack of explanations. This paper addresses the post-hoc BO explainability problem for cyber-physical systems. We introduce TNTRules (Tune-No-Tune Rules), a novel algorithm that provides both global and local explanations for BO recommendations. TNTRules generates actionable rules and visual graphs, identifying optimal solution bounds and ranges, as well as potential alternative solutions. Unlike existing explainable AI (XAI) methods, TNTRules is tailored specifically for BO, by encoding uncertainty via a variance pruning technique and hierarchical agglomerative clustering. A multi-objective optimization approach allows maximizing explanation quality. We evaluate TNTRules using established XAI metrics (Correctness, Completeness, and Compactness) and compare it against adapted baseline methods. The results demonstrate that TNTRules generates high-fidelity, compact, and complete explanations, significantly outperforming three baselines on 5 multi-objective testing functions and 2 hyperparameter tuning problems.
Interactive Machine Learning (IML) seeks to integrate human expertise into machine learning processes. However, most existing algorithms cannot be applied to Realworld Scenarios because their state spaces and/or action spaces are limited to discrete values. Furthermore, the interaction of all existing methods is restricted to deciding between multiple proposals. We therefore propose a novel framework based on Bayesian Optimization (BO). Interactive Bayesian Optimization (IBO) enables collaboration between machine learning algorithms and humans. This framework captures user preferences and provides an interface for users to shape the strategy by hand. Additionally, we've incorporated a new acquisition function, Preference Expected Improvement (PEI), to refine the system's efficiency using a probabilistic model of the user preferences. Our approach is geared towards ensuring that machines can benefit from human expertise, aiming for a more aligned and effective learning process. In the course of this work, we applied our method to simulations and in a real world task using a Franka Panda robot to show human-robot collaboration.
State-of-the-art vehicle dynamics estimation techniques usually share one common drawback: each variable to estimate is computed with an independent, simplified filtering module. These modules run in parallel and need to be calibrated separately. To solve this issue, a unified Twin-in-the-Loop (TiL) Observer architecture has recently been proposed: the classical simplified control-oriented vehicle model in the estimators is replaced by a full-fledged vehicle simulator, or digital twin (DT). The states of the DT are corrected in real time with a linear time invariant output error law. Since the simulator is a black-box, no explicit analytical formulation is available, hence classical filter tuning techniques cannot be used. Due to this reason, Bayesian Optimization will be used to solve a data-driven optimization problem to tune the filter. Due to the complexity of the DT, the optimization problem is high-dimensional. This paper aims to find a procedure to tune the high-complexity observer by lowering its dimensionality. In particular, in this work we will analyze both a supervised and an unsupervised learning approach. The strategies have been validated for speed and yaw-rate estimation on real-world data.
Unsupervised representation learning presents new opportunities for advancing Quantum Architecture Search (QAS) on Noisy Intermediate-Scale Quantum (NISQ) devices. QAS is designed to optimize quantum circuits for Variational Quantum Algorithms (VQAs). Most QAS algorithms tightly couple the search space and search algorithm, typically requiring the evaluation of numerous quantum circuits, resulting in high computational costs and limiting scalability to larger quantum circuits. Predictor-based QAS algorithms mitigate this issue by estimating circuit performance based on structure or embedding. However, these methods often demand time-intensive labeling to optimize gate parameters across many circuits, which is crucial for training accurate predictors. Inspired by the classical neural architecture search algorithm Arch2vec, we investigate the potential of unsupervised representation learning for QAS without relying on predictors. Our framework decouples unsupervised architecture representation learning from the search process, enabling the learned representations to be applied across various downstream tasks. Additionally, it integrates an improved quantum circuit graph encoding scheme, addressing the limitations of existing representations and enhancing search efficiency. This predictor-free approach removes the need for large labeled datasets. During the search, we employ REINFORCE and Bayesian Optimization to explore the latent representation space and compare their performance against baseline methods. We further validate our approach by executing the best-discovered MaxCut circuits on IBM's ibm_sherbrooke quantum processor, confirming that the architectures retain optimal performance even under real hardware noise. Our results demonstrate that the framework efficiently identifies high-performing quantum circuits with fewer search iterations.
Bayesian Optimization (BO) is a powerful method for optimizing black-box functions by combining prior knowledge with ongoing function evaluations. BO constructs a probabilistic surrogate model of the objective function given the covariates, which is in turn used to inform the selection of future evaluation points through an acquisition function. For smooth continuous search spaces, Gaussian Processes (GPs) are commonly used as the surrogate model as they offer analytical access to posterior predictive distributions, thus facilitating the computation and optimization of acquisition functions. However, in complex scenarios involving optimization over categorical or mixed covariate spaces, GPs may not be ideal. This paper introduces Simulation Based Bayesian Optimization (SBBO) as a novel approach to optimizing acquisition functions that only requires sampling-based access to posterior predictive distributions. SBBO allows the use of surrogate probabilistic models tailored for combinatorial spaces with discrete variables. Any Bayesian model in which posterior inference is carried out through Markov chain Monte Carlo can be selected as the surrogate model in SBBO. We demonstrate empirically the effectiveness of SBBO using various choices of surrogate models in applications involving combinatorial optimization. choices of surrogate models.
Solving large-scale capacity expansion problems (CEPs) is central to cost-effective decarbonization of regional-scale energy systems. To ensure the intended outcomes of CEPs, modeling uncertainty due to weather-dependent variable renewable energy (VRE) supply and energy demand becomes crucially important. However, the resulting stochastic optimization models are often less computationally tractable than their deterministic counterparts. Here, we propose a learning-assisted approximate solution method to tractably solve two-stage stochastic CEPs. Our method identifies low-cost planning decisions by constructing and solving a sequence of tractable temporally aggregated surrogate problems. We adopt a Bayesian optimization approach to searching the space of time series aggregation hyperparameters and compute approximate solutions that minimize costs on a validation set of supply-demand projections. Importantly, we evaluate solved planning outcomes on a held-out set of test projections. We apply our approach to generation and transmission expansion planning for a joint power-gas system spanning New England. We show that our approach yields an estimated cost savings of up to 3.8% in comparison to benchmark time series aggregation approaches.
This work introduces a framework to address the computational complexity inherent in Mixed-Integer Programming (MIP) models by harnessing the potential of deep learning. By employing deep learning, we construct problem-specific heuristics that identify and exploit common structures across MIP instances. We train deep learning models to estimate complicating binary variables for target MIP problem instances. The resulting reduced MIP models are solved using standard off-the-shelf solvers. We present an algorithm for generating synthetic data enhancing the robustness and generalizability of our models across diverse MIP instances. We compare the effectiveness of (a) feed-forward neural networks (ANN) and (b) convolutional neural networks (CNN). To enhance the framework's performance, we employ Bayesian optimization for hyperparameter tuning, aiming to maximize the occurrence of global optimum solutions. We apply this framework to a flow-based facility location allocation MIP formulation that describes long-term investment planning and medium-term tactical scheduling in a personalized medicine supply chain.
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to conditioning. We explore stochastic gradient algorithms as a computationally efficient method of approximately solving these linear systems: we develop low-variance optimization objectives for sampling from the posterior and extend these to inducing points. Counterintuitively, stochastic gradient descent often produces accurate predictions, even in cases where it does not converge quickly to the optimum. We explain this through a spectral characterization of the implicit bias from non-convergence. We show that stochastic gradient descent produces predictive distributions close to the true posterior both in regions with sufficient data coverage, and in regions sufficiently far away from the data. Experimentally, stochastic gradient descent achieves state-of-the-art performance on sufficiently large-scale or ill-conditioned regression tasks. Its uncertainty estimates match the performance of significantly more expensive baselines on a large-scale Bayesian optimization task.
In this paper, we study the problem of estimating the normalizing constant $\int e^{-\lambda f(x)}dx$ through queries to the black-box function $f$, where $f$ belongs to a reproducing kernel Hilbert space (RKHS), and $\lambda$ is a problem parameter. We show that to estimate the normalizing constant within a small relative error, the level of difficulty depends on the value of $\lambda$: When $\lambda$ approaches zero, the problem is similar to Bayesian quadrature (BQ), while when $\lambda$ approaches infinity, the problem is similar to Bayesian optimization (BO). More generally, the problem varies between BQ and BO. We find that this pattern holds true even when the function evaluations are noisy, bringing new aspects to this topic. Our findings are supported by both algorithm-independent lower bounds and algorithmic upper bounds, as well as simulation studies conducted on a variety of benchmark functions.
The continued growth in the deployment of Internet-of-Things (IoT) devices has been fueled by the increased connectivity demand, particularly in industrial environments. However, this has led to an increase in the number of network related attacks due to the increased number of potential attack surfaces. Industrial IoT (IIoT) devices are prone to various network related attacks that can have severe consequences on the manufacturing process as well as on the safety of the workers in the manufacturing plant. One promising solution that has emerged in recent years for attack detection is Machine learning (ML). More specifically, ensemble learning models have shown great promise in improving the performance of the underlying ML models. Accordingly, this paper proposes a framework based on the combined use of Bayesian Optimization-Gaussian Process (BO-GP) with an ensemble tree-based learning model to improve the performance of intrusion and attack detection in IIoT environments. The proposed framework's performance is evaluated using the Windows 10 dataset collected by the Cyber Range and IoT labs at University of New South Wales. Experimental results illustrate the improvement in detection accuracy, precision, and F-score when compared to standard tree and ensemble tree models.
The creation of low-order dynamic models for complex industrial systems is complicated by disturbances and limited sensor accuracy. This work presents a system identification procedure that uses machine learning methods and process knowledge to robustly identify a low-order closed-loop model of a municipal solid waste (MSW) grate incineration plant. These types of plants are known for their strong disturbances coming from fuel composition fluctuations. Using Bayesian optimization, the algorithm ranks and selects inputs from the available sensor data and chooses the model structure. This results in accurate models with low complexity while avoiding overfitting. The method is applied and validated using data of an industrial MSW incineration plant. The obtained models give excellent predictions and confidence intervals for the steam capacity and intermediate quantities such as supply air flow and flue gas temperature. The identified continuous-time models are fully given, and their step-response dynamics are discussed. The models can be used to develop model-based unit control schemes for grate incineration plants. The presented method shows great potential for the identification of over-actuated systems or disturbed systems with many sensors.
This study proposes a Newton based multiple objective optimization algorithm for hyperparameter search. The first order differential (gradient) is calculated using finite difference method and a gradient matrix with vectorization is formed for fast computation. The Newton Raphson iterative solution is used to update model parameters with iterations, and a regularization term is included to eliminate the singularity issue. The algorithm is applied to search the optimal probability threshold (a vector of eight parameters) for a multiclass object detection problem of a convolutional neural network. The algorithm quickly finds the improved parameter values to produce an overall higher true positive (TP) and lower false positive (FP) rates, as compared to using the default value of 0.5. In comparison, the Bayesian optimization generates lower performance in the testing case. However, the performance and parameter values may oscillate for some cases during iterations, which may be due to the data driven stochastic nature of the subject. Therefore, the optimal parameter value can be identified from a list of iteration steps according to the optimal TP and FP results.
Neural Architecture Search (NAS) methods are widely used in various industries to obtain high quality taskspecific solutions with minimal human intervention. Event Sequences find widespread use in various industrial applications including churn prediction customer segmentation fraud detection and fault diagnosis among others. Such data consist of categorical and real-valued components with irregular timestamps. Despite the usefulness of NAS methods previous approaches only have been applied to other domains images texts or time series. Our work addresses this limitation by introducing a novel NAS algorithm SeqNAS specifically designed for event sequence classification. We develop a simple yet expressive search space that leverages commonly used building blocks for event sequence classification including multihead self attention convolutions and recurrent cells. To perform the search we adopt sequential Bayesian Optimization and utilize previously trained models as an ensemble of teachers to augment knowledge distillation. As a result of our work we demonstrate that our method surpasses state of the art NAS methods and popular architectures suitable for sequence classification and holds great potential for various industrial applications.
Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking Gaussian process posteriors and need to partition the optimization problem into small regions to ensure exploration or assume an underlying low-dimensional structure. With the idea of transiting the candidate points towards more promising positions, we propose a new method based on Markov Chain Monte Carlo to efficiently sample from an approximated posterior. We provide theoretical guarantees of its convergence in the Gaussian process Thompson sampling setting. We also show experimentally that both the Metropolis-Hastings and the Langevin Dynamics version of our algorithm outperform state-of-the-art methods in high-dimensional sequential optimization and reinforcement learning benchmarks.
Bayesian optimization is a principled optimization strategy for a black-box objective function. It shows its effectiveness in a wide variety of real-world applications such as scientific discovery and experimental design. In general, the performance of Bayesian optimization is reported through regret-based metrics such as instantaneous, simple, and cumulative regrets. These metrics only rely on function evaluations, so that they do not consider geometric relationships between query points and global solutions, or query points themselves. Notably, they cannot discriminate if multiple global solutions are successfully found. Moreover, they do not evaluate Bayesian optimization's abilities to exploit and explore a search space given. To tackle these issues, we propose four new geometric metrics, i.e., precision, recall, average degree, and average distance. These metrics allow us to compare Bayesian optimization algorithms considering the geometry of both query points and global optima, or query points. However, they are accompanied by an extra parameter, which needs to be carefully determined. We therefore devise the parameter-free forms of the respective metrics by integrating out the additional parameter. Finally, we validate that our proposed metrics can provide more delicate interpretation of Bayesian optimization, on top of assessment via the conventional metrics.
Sample efficiency is crucial in optimization, particularly in black-box scenarios characterized by expensive evaluations and zeroth-order feedback. When computing resources are plentiful, Bayesian optimization is often favored over evolution strategies. In this paper, we introduce a full invariance oriented evolution strategies algorithm, derived from its corresponding framework, that effectively rivals the leading Bayesian optimization method in tasks with dimensions at the upper limit of Bayesian capability. Specifically, we first build the framework InvIGO that fully incorporates historical information while retaining the full invariant and computational complexity. We then exemplify InvIGO on multi-dimensional Gaussian, which gives an invariant and scalable optimizer SynCMA . The theoretical behavior and advantages of our algorithm over other Gaussian-based evolution strategies are further analyzed. Finally, We benchmark SynCMA against leading algorithms in Bayesian optimization and evolution strategies on various high dimension tasks, in cluding Mujoco locomotion tasks, rover planning task and synthetic functions. In all scenarios, SynCMA demonstrates great competence, if not dominance, over other algorithms in sample efficiency, showing the underdeveloped potential of property oriented evolution strategies.