Bayesian optimization package: PHYSBO

Bayesian optimization (BO) is a versatile and robust global optimization method under uncertainty. However, most of the BO algorithms were developed for problems with only continuous variables. For practical engineering optimization, discrete variables are also prevalent. BO methods based on Gaussian process (GP) surrogates also suffers from the curse-of-dimensionality problem. To address these challenges, in this paper, a Bayesian discrete optimization algorithm is introduced to solve permutation-based combinatorial problems. A new kernel function is developed based on position distances for permutation. To improve the efficiency and scalability of the algorithm, a sparse GP model based on inducing points is further developed, where the simulated annealing algorithm is applied to select inducing points. The new algorithm is demonstrated and tested with the production scheduling problem for additive manufacturing. Experimental results show that the proposed algorithm can find a better solution with limited evaluations than state-of-the-art algorithms.

This paper incorporates Bayesian estimation and optimization into a portfolio selection framework, particularly for high-dimensional portfolios in which the number of assets is larger than the number of observations. We leverage a constrained minimization approach, called the linear programming optimal (LPO) portfolio, to directly estimate effective parameters appearing in the optimal portfolio. We propose two refinements for the LPO strategy. First, we explore improved Bayesian estimates, instead of sample estimates, of the covariance matrix of asset returns. Second, we introduce Bayesian optimization (BO) to replace traditional grid-search cross-validation (CV) in tuning hyperparameters of the LPO strategy. We further propose modifications in the BO algorithm by (1) taking into account the time-dependent nature of financial problems and (2) extending the commonly used expected improvement acquisition function to include a tunable trade-off with the improvement’s variance. Allowing a general case of noisy observations, we theoretically derive the sublinear convergence rate of BO under the newly proposed EIVar and thus our algorithm has no regret. Our empirical studies confirm that the adjusted BO results in portfolios with higher out-of-sample Sharpe ratio, certainty equivalent, and lower turnover compared to those tuned with CV. This superior performance is achieved with a significant reduction in time elapsed, thus also addressing time-consuming issues of CV. Furthermore, LPO with Bayesian estimates outperforms the original proposal of LPO, as well as the benchmark equally weighted and plugin strategies.

Brain tumor is one of the most aggressive diseases nowadays, resulting in a very short life span if it is diagnosed at an advanced stage. The treatment planning phase is thus essential for enhancing the quality of life for patients. The use of Magnetic Resonance Imaging (MRI) in the diagnosis of brain tumors is extremely widespread, but the manual interpretation of large amounts of images requires considerable effort and is prone to human errors. Hence, an automated method is necessary to identify the most common brain tumors. Convolutional Neural Network (CNN) architectures are successful in image classification due to their high layer count, which enables them to conceive the features effectively on their own. The tuning of CNN hyperparameters is critical in every dataset since it has a significant impact on the efficiency of the training model. Given the high dimensionality and complexity of the data, manual hyperparameter tuning would take an inordinate amount of time, with the possibility of failing to identify the optimal hyperparameters. In this paper, we proposed a Bayesian Optimization-based efficient hyperparameter optimization technique for CNN. This method was evaluated by classifying 3064 T-1-weighted CE-MRI images into three types of brain tumors (Glioma, Meningioma, and Pituitary). Based on Transfer Learning, the performance of five well-recognized deep pre-trained models is compared with that of the optimized CNN. After using Bayesian Optimization, our CNN was able to attain 98.70% validation accuracy at best without data augmentation or cropping lesion techniques, while VGG16, VGG19, ResNet50, InceptionV3, and DenseNet201 achieved 97.08%, 96.43%, 89.29%, 92.86%, and 94.81% validation accuracy, respectively. Moreover, the proposed model outperforms state-of-the-art methods on the CE-MRI dataset, demonstrating the feasibility of automating hyperparameter optimization.

Aim/Purpose: Traditional hyperparameter tuning methods’ inefficiency and low accuracy in diabetes prediction. Application and evaluation of Bayesian optimization aim to increase the accuracy of diabetes prediction models. Background: Bayesian optimization (BO) has emerged as a powerful technique for hyperparameter tuning in machine learning models with its methodical approach for optimizing complex functions with expensive evaluations. Selecting the optimal hyperparameters for models can significantly increase prediction accuracy in the healthcare sector, particularly for diabetes prediction, hence improving patient outcomes and resource management. Methodology: Among the well-known diabetes databases used in the study is the Pima Indian Diabetes Database. Among the machine learning models developed and whose hyperparameters are modified via Bayesian optimization are Support Vector Machines (SVM), Random Forest, and Gradient Boosting Machines (GBM). The optimization process is compared with traditional tuning methods to assess improvements in model performance. Contribution: Problems include the increasing prevalence of diabetes worldwide and the role vital function prediction models play in early diagnosis and therapy. Especially when dealing with enormous datasets common in healthcare, grid search, and random search are sometimes computationally taxing and inefficient. However, Bayesian optimization promises a more practical and economical approach by selecting hyperparameters iteratively based on earlier evaluations. Findings: Bayesian optimization not only yields faster calculation times but also outperforms traditional methods. More precisely, models adapted by Bayesian optimization show greater sensitivity and specificity, which are crucial for accurate and prompt diabetes diagnosis. Recommendation for Researchers: By highlighting the specific elements and network characteristics that are behind the anomalies it discovers, on a real-time or large scale dataset. Future Research: This work can be improvised using several recent artificial intelligence algorithms with the integration of IoT on real-time datasets.

Abstarct Engineering design problems typically require optimizing a quality measure by finding the right combination of controllable input parameters. In Additive Manufacturing (AM), the output characteristics of the process can often be non-stationary functions of the process parameters. Bayesian Optimization (BO) is a methodology to optimize such “black-box” functions, i.e., the input–output relationship is unknown and expensive to compute. Optimization tasks involving “black-box” functions widely use BO with Gaussian Process (GP) regression surrogate model. Using GPs with standard kernels is insufficient for modeling non-stationary functions, while GPs with non-stationary kernels are typically over-parameterized. On the other hand, a Deep Gaussian Process (DGP) can overcome GPs’ shortcomings by considering a composition of multiple GPs. Inference in a DGP is challenging due to its structure resulting in a non-Gaussian posterior, and using DGP as a surrogate model for BO is not straightforward. Stochastic Imputation (SI)-based inference is promising in speed and accuracy for BO. This work proposes a bootstrap aggregation-based procedure to effectively utilize the SI-based inference for BO with a DGP surrogate model. The proposed BO algorithm DGP-SI-BO is faster and empirically better than the state-of-the-art BO method in optimizing non-stationary functions. Several analytical test functions and a case study in metal AM simulation demonstrate the applicability of the proposed method.

Bayesian optimization seeks the global optimum of a black-box, objective function f (x), in the fewest possible iterations. Recent work applied knowledge of the true value of the optimum to the Gaussian Process probabilistic model typically used in Bayesian optimization. This, together with a new acquisition function called Confidence Bound Minimization, resulted in a Gaussian probabilistic posterior in which the predictions were no greater than the known maximum (and no less than for minimum). Our novel work applies Confidence Bound Minimization to Bayesian optimization with Student's-t Processes, a probabilistic alternative which addresses known weaknesses in Gaussian Processes - outliers' probability and the calculation of posterior covariance. The new model is applied to the problem of hyperparameter tuning for an XGBoost classifier. Experiments show superior regret minimization and predictive accuracy, versus the popular Expected Improvement acquisition function. Combining Confidence Bound Minimization with a transformed Student's-t Process probabilistic model and known optima produces superior training regret minimization and posterior predictions for the Six-Hump Camel(2D) and Levy(4D) benchmark problems, which do not fall below true minima.

Financial Applications of Gaussian Processes and Bayesian Optimization

Designing preference elicitation (PE) methodologies that can quickly ascertain a user’s top item preferences in a cold-start setting is a key challenge for building effective and personalized conversational recommendation (ConvRec) systems. While large language models (LLMs) enable fully natural language (NL) PE dialogues, we hypothesize that monolithic LLM NL-PE approaches lack the multi-turn, decision-theoretic reasoning required to effectively balance the exploration and exploitation of user preferences towards an arbitrary item set. In contrast, traditional Bayesian optimization PE methods define theoretically optimal PE strategies, but cannot generate arbitrary NL queries or reason over content in NL item descriptions – requiring users to express preferences via ratings or comparisons of unfamiliar items. To overcome the limitations of both approaches, we formulate NL-PE in a Bayesian Optimization (BO) framework that seeks to actively elicit NL feedback to identify the best recommendation. Key challenges in generalizing BO to deal with natural language feedback include determining: (a) how to leverage LLMs to model the likelihood of NL preference feedback as a function of item utilities, and (b) how to design an acquisition function for NL BO that can elicit preferences in the infinite space of language. We demonstrate our framework in a novel NL-PE algorithm, PEBOL, which uses: 1) Natural Language Inference (NLI) between user preference utterances and NL item descriptions to maintain Bayesian preference beliefs, and 2) BO strategies such as Thompson Sampling (TS) and Upper Confidence Bound (UCB) to guide LLM query generation. We numerically evaluate our methods in controlled simulations, finding that after 10 turns of dialogue, PEBOL can achieve an MRR@10 of up to 0.27 compared to the best monolithic LLM baseline’s MRR@10 of 0.17, despite relying on earlier and smaller LLMs.1

This study presents a data-driven approach for optimizing the operating altitude of Airborne Wind Energy (AWE) systems to maximize net energy production. Determining the optimal operating altitude of an AWE system is challenging, as the wind speed constantly varies with both time and altitude. Furthermore, without expensive auxiliary equipment, the wind speed is only measurable at the AWE system's operating altitude. The work presented in this paper shows how tools from machine learning can be blended with real-time control to optimize the AWE system's operating altitude efficiently, without the use of auxiliary wind profiling equipment. Specifically, Bayesian Optimization, which is a data-driven technique for finding the optimum of an unknown and expensive-to-evaluate objective function, is applied to the real-time control of an AWE system. The underlying objective function is modeled by a Gaussian Process (GP); then, Bayesian Optimization utilizes the predictive uncertainty information from the GP to decide the best subsequent operating altitude. In the AWE application, conventional Bayesian Optimization is extended to handle the time-varying nature of the wind shear profile (wind speed vs. time). Using real wind data, our method is validated against three baseline approaches. Our simulation results show that the Bayesian Optimization method is successful in dramatically increasing power production over these baselines.

Bayesian optimization has emerged at the forefront of expensive black-box optimization due to its data efficiency. Recent years have witnessed a proliferation of studies on the development of new Bayesian optimization algorithms and their applications. Hence, this article attempts to provide a comprehensive and updated survey of recent advances in Bayesian optimization that are mainly based on Gaussian processes and identify challenging open problems. We categorize the existing work on Bayesian optimization into nine main groups according to the motivations and focus of the proposed algorithms. For each category, we present the main advances with respect to the construction of surrogate models and adaptation of the acquisition functions. Finally, we discuss the open questions and suggest promising future research directions, in particular with regard to heterogeneity, privacy preservation, and fairness in distributed and federated optimization systems.

We consider an autonomous exploration problem in which a mobile robot is guided by an information-based controller through an a priori unknown environment, choosing to collect its next measurement at the location estimated to be most informative within its current field of view. We propose a novel approach to predict mutual information (MI) using Bayesian optimization. Over several iterations, candidate sensing actions are suggested by Bayesian optimization and added to a committee that repeatedly trains a Gaussian process (GP). The GP estimates MI throughout the robot's action space, serving as the basis for an acquisition function used to select the next candidate. The best sensing action in the committee is executed by the robot. This approach is compared over several environments with two batch methods, one which chooses the most informative action from a set of pseudo-random samples whose MI is explicitly evaluated, and one that applies GP regression to this sample set. Our computational results demonstrate that the proposed method provides not only computational efficiency and rapid map entropy reduction, but also robustness in comparison with competing approaches.

This paper describes a method combining Bayesian optimization (BO) and a lumped-capacitance thermal network model that is effective for speeding up the thermal design optimization of an electronic circuit board layout with transient heating chips. As electronic devices have become smaller and more complex, the importance of thermal design optimization to ensure heat dissipation performance has increased. However, such a thermal design optimization is difficult because various trade-offs associated with packaging and transient temperature changes of heat-generating components must be considered. This study aims to improve the performance of thermal design optimization by artificial intelligence. BO using a Gaussian process was combined with the lumped-capacitance thermal network model, and its performance was verified. As a result, BO successfully found the ideal circuit board layout as well as particle swarm optimization (PSO) and genetic algorithm (GA) could. The CPU time for BO was 1/5 and 1/4 of that for PSO and GA. In addition, BO found a non-intuitive optimal solution in approximately 7 min from 10 million layout patterns. It was estimated that this was 1/1000 of the CPU time required for analyzing all layout patterns.

Bayesian Optimization (BO) has been widely applied to optimize expensive black-box functions while retaining sample efficiency. However, scaling BO to high-dimensional spaces remains challenging. Existing literature proposes performing standard BO in multiple local trust regions (TuRBO) for heterogeneous modeling of the objective function and avoiding over-exploration. Despite its advantages, using local Gaussian Processes (GPs) reduces sampling efficiency compared to a global GP. To enhance sampling efficiency while preserving heterogeneous modeling, we propose to construct multiple local quadratic models using gradients and Hessians from a global GP, and select new sample points by solving the bound-constrained quadratic program. Additionally, we address the issue of vanishing gradients of GPs in high-dimensional spaces. We provide a convergence analysis and demonstrate through experimental results that our method enhances the efficacy of TuRBO and outperforms a wide range of high-dimensional BO techniques on synthetic functions and real-world applications.

Bayesian optimization for congestion pricing problems: A general framework and its instability

We propose an extrinsic Bayesian optimization (eBO) framework for general optimization problems on manifolds. Bayesian optimization algorithms build a surrogate of the objective function by employing Gaussian processes and utilizing the uncertainty in that surrogate by deriving an acquisition function. This acquisition function represents the probability of improvement based on the kernel of the Gaussian process, which guides the search in the optimization process. The critical challenge for designing Bayesian optimization algorithms on manifolds lies in the difficulty of constructing valid covariance kernels for Gaussian processes on general manifolds. Our approach is to employ extrinsic Gaussian processes by first embedding the manifold onto some higher dimensional Euclidean space via equivariant embeddings and then constructing a valid covariance kernel on the image manifold after the embedding. This leads to efficient and scalable algorithms for optimization over complex manifolds. Simulation study and real data analyses are carried out to demonstrate the utilities of our eBO framework by applying the eBO to various optimization problems over manifolds such as the sphere, the Grassmannian, and the manifold of positive definite matrices.