We propose a nested weighted Tchebycheff Multi-objective Bayesian optimization framework where we build a regression model selection procedure from an ensemble of models, towards better estimation of the uncertain parameters of the weighted-Tchebycheff expensive black-box multi-objective function. In existing work, a weighted Tchebycheff MOBO approach has been demonstrated which attempts to estimate the unknown utopia in formulating acquisition function, through calibration using a priori selected regression model. However, the existing MOBO model lacks flexibility in selecting the appropriate regression models given the guided sampled data and therefore, can under-fit or over-fit as the iterations of the MOBO progress, reducing the overall MOBO performance. As it is too complex to a priori guarantee a best model in general, this motivates us to consider a portfolio of different families of predictive models fitted with current training data, guided by the WTB MOBO; the best model is selected following a user-defined prediction root mean-square-error-based approach. The proposed approach is implemented in optimizing a multi-modal benchmark problem and a thin tube design under constant loading of temperature-pressure, with minimizing the risk of creep-fatigue failure and design cost. Finally, the nested weighted Tchebycheff MOBO model performance is compared with different MOBO frameworks with respect to accuracy in parameter estimation, Pareto-optimal solutions and function evaluation cost. This method is generalized enough to consider different families of predictive models in the portfolio for best model selection, where the overall design architecture allows for solving any high-dimensional (multiple functions) complex black-box problems and can be extended to any other global criterion multi-objective optimization methods where prior knowledge of utopia is required.
Designing neural architectures requires immense manual efforts. This has promoted the development of neural architecture search (NAS) to automate the design. While previous NAS methods achieve promising results but run slowly, zero-cost proxies run extremely fast but are less promising. Therefore, it is of great potential to accelerate NAS via those zero-cost proxies. The existing method has two limitations, which are unforeseeable reliability and one-shot usage. To address the limitations, we present ProxyBO, an efficient Bayesian optimization (BO) framework that utilizes the zero-cost proxies to accelerate neural architecture search. We apply the generalization ability measurement to estimate the fitness of proxies on the task during each iteration and design a novel acquisition function to combine BO with zero-cost proxies based on their dynamic influence. Extensive empirical studies show that ProxyBO consistently outperforms competitive baselines on five tasks from three public benchmarks. Concretely, ProxyBO achieves up to 5.41x and 3.86x speedups over the state-of-the-art approaches REA and BRP-NAS.
Data-efficient learning algorithms are essential in many practical applications for which data collection is expensive, e.g., for the optimal deployment of wireless systems in unknown propagation scenarios. Meta-learning can address this problem by leveraging data from a set of related learning tasks, e.g., from similar deployment settings. In practice, one may have available only unlabeled data sets from the related tasks, requiring a costly labeling procedure to be carried out before use in meta-learning. For instance, one may know the possible positions of base stations in a given area, but not the performance indicators achievable with each deployment. To decrease the number of labeling steps required for meta-learning, this paper introduces an information-theoretic active task selection mechanism, and evaluates an instantiation of the approach for Bayesian optimization of black-box models.
One way to reduce the time of conducting optimization studies is to evaluate designs in parallel rather than just one-at-a-time. For expensive-to-evaluate black-boxes, batch versions of Bayesian optimization have been proposed. They work by building a surrogate model of the black-box to simultaneously select multiple designs via an infill criterion. Still, despite the increased availability of computing resources that enable large-scale parallelism, the strategies that work for selecting a few tens of parallel designs for evaluations become limiting due to the complexity of selecting more designs. It is even more crucial when the black-box is noisy, necessitating more evaluations as well as repeating experiments. Here we propose a scalable strategy that can keep up with massive batching natively, focused on the exploration/exploitation trade-off and a portfolio allocation. We compare the approach with related methods on noisy functions, for mono and multi-objective optimization tasks. These experiments show orders of magnitude speed improvements over existing methods with similar or better performance.
Bayesian optimization (BO) is an effective approach to optimize expensive black-box functions, that seeks to trade-off between exploitation (selecting parameters where the maximum is likely) and exploration (selecting parameters where we are uncertain about the objective function). In many real-world situations, direct measurements of the objective function are not possible, and only binary measurements such as success/failure or pairwise comparisons are available. To perform efficient exploration in this setting, we show that it is important for BO algorithms to distinguish between different types of uncertainty: epistemic uncertainty, about the unknown objective function, and aleatoric uncertainty, which comes from noisy observations and cannot be reduced. In effect, only the former is important for efficient exploration. Based on this, we propose several new acquisition functions that outperform state-of-the-art heuristics in binary and preferential BO, while being fast to compute and easy to implement. We then generalize these acquisition rules to batch learning, where multiple queries are performed simultaneously.
Federated Learning (FL) decouples model training from the need for direct access to the data and allows organizations to collaborate with industry partners to reach a satisfying level of performance without sharing vulnerable business information. The performance of a machine learning algorithm is highly sensitive to the choice of its hyperparameters. In an FL setting, hyperparameter optimization poses new challenges. In this work, we investigated the impact of different hyperparameter optimization approaches in an FL system. In an effort to reduce communication costs, a critical bottleneck in FL, we investigated a local hyperparameter optimization approach that -- in contrast to a global hyperparameter optimization approach -- allows every client to have its own hyperparameter configuration. We implemented these approaches based on grid search and Bayesian optimization and evaluated the algorithms on the MNIST data set using an i.i.d. partition and on an Internet of Things (IoT) sensor based industrial data set using a non-i.i.d. partition.
We consider the problem of black-box multi-objective optimization (MOO) using expensive function evaluations (also referred to as experiments), where the goal is to approximate the true Pareto set of solutions by minimizing the total resource cost of experiments. For example, in hardware design optimization, we need to find the designs that trade-off performance, energy, and area overhead using expensive computational simulations. The key challenge is to select the sequence of experiments to uncover high-quality solutions using minimal resources. In this paper, we propose a general framework for solving MOO problems based on the principle of output space entropy (OSE) search: select the experiment that maximizes the information gained per unit resource cost about the true Pareto front. We appropriately instantiate the principle of OSE search to derive efficient algorithms for the following four MOO problem settings: 1) The most basic em single-fidelity setting, where experiments are expensive and accurate; 2) Handling em black-box constraints} which cannot be evaluated without performing experiments; 3) The discrete multi-fidelity setting, where experiments can vary in the amount of resources consumed and their evaluation accuracy; and 4) The em continuous-fidelity setting, where continuous function approximations result in a huge space of experiments. Experiments on diverse synthetic and real-world benchmarks show that our OSE search based algorithms improve over state-of-the-art methods in terms of both computational-efficiency and accuracy of MOO solutions.
We study the problem of performance optimization of closed-loop control systems with unmodeled dynamics. Bayesian optimization (BO) has been demonstrated 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. In this paper, we propose a violation-aware BO algorithm (VABO) that optimizes closed-loop performance while simultaneously learning constraint-feasible solutions. Unlike classical constrained BO methods which allow an 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 VABO method for energy minimization of industrial vapor compression systems.
We propose a surrogate-assisted reference vector adaptation (SRVA) method to solve expensive multi- and many-objective optimization problems with various Pareto front shapes. SRVA is coupled with a multi-objective Bayesian optimization (MBO) algorithm using reference vectors for scalarization of objective functions. The Kriging surrogate models for MBO is used to estimate the Pareto front shape and generate adaptive reference vectors uniformly distributed on the estimated Pareto front. We combine SRVA with expected improvement of penalty-based boundary intersection as an infill criterion for MBO. The proposed algorithm is compared with two other MBO algorithms by applying them to benchmark problems with various Pareto front shapes. Experimental results show that the proposed algorithm outperforms the other two in the problems whose objective functions are reasonably approximated by the Kriging models. SRVA improves diversity of non-dominated solutions for these problems with continuous, discontinuous, and degenerated Pareto fronts. Besides, the proposed algorithm obtains much better solutions from early stages of optimization especially in many-objective problems.
We introduce the algorithm Bayesian Optimization (BO) with Fictitious Play (BOFiP) for the optimization of high dimensional black box functions. BOFiP decomposes the original, high dimensional, space into several sub-spaces defined by non-overlapping sets of dimensions. These sets are randomly generated at the start of the algorithm, and they form a partition of the dimensions of the original space. BOFiP searches the original space with alternating BO, within sub-spaces, and information exchange among sub-spaces, to update the sub-space function evaluation. The basic idea is to distribute the high dimensional optimization across low dimensional sub-spaces, where each sub-space is a player in an equal interest game. At each iteration, BO produces approximate best replies that update the players belief distribution. The belief update and BO alternate until a stopping condition is met. High dimensional problems are common in real applications, and several contributions in the BO literature have highlighted the difficulty in scaling to high dimensions due to the computational complexity associated to the estimation of the model hyperparameters. Such complexity is exponential in the problem dimension, resulting in substantial loss of performance for most techniques with the increase of the input dimensionality. We compare BOFiP to several state-of-the-art approaches in the field of high dimensional black box optimization. The numerical experiments show the performance over three benchmark objective functions from 20 up to 1000 dimensions. A neural network architecture design problem is tested with 42 up to 911 nodes in 6 up to 92 layers, respectively, resulting into networks with 500 up to 10,000 weights. These sets of experiments empirically show that BOFiP outperforms its competitors, showing consistent performance across different problems and increasing problem dimensionality.
Offline reinforcement learning enables agents to leverage large pre-collected datasets of environment transitions to learn control policies, circumventing the need for potentially expensive or unsafe online data collection. Significant progress has been made recently in offline model-based reinforcement learning, approaches which leverage a learned dynamics model. This typically involves constructing a probabilistic model, and using the model uncertainty to penalize rewards where there is insufficient data, solving for a pessimistic MDP that lower bounds the true MDP. Existing methods, however, exhibit a breakdown between theory and practice, whereby pessimistic return ought to be bounded by the total variation distance of the model from the true dynamics, but is instead implemented through a penalty based on estimated model uncertainty. This has spawned a variety of uncertainty heuristics, with little to no comparison between differing approaches. In this paper, we compare these heuristics, and design novel protocols to investigate their interaction with other hyperparameters, such as the number of models, or imaginary rollout horizon. Using these insights, we show that selecting these key hyperparameters using Bayesian Optimization produces superior configurations that are vastly different to those currently used in existing hand-tuned state-of-the-art methods, and result in drastically stronger performance.
We discuss the correspondence between Gaussian process regression and Geometric Harmonics, two similar kernel-based methods that are typically used in different contexts. Research communities surrounding the two concepts often pursue different goals. Results from both camps can be successfully combined, providing alternative interpretations of uncertainty in terms of error estimation, or leading towards accelerated Bayesian Optimization due to dimensionality reduction.
Perovskite photovoltaics (PV) have achieved rapid development in the past decade in terms of power conversion efficiency of small-area lab-scale devices; however, successful commercialization still requires further development of low-cost, scalable, and high-throughput manufacturing techniques. One of the critical challenges of developing a new fabrication technique is the high-dimensional parameter space for optimization, but machine learning (ML) can readily be used to accelerate perovskite PV scaling. Herein, we present an ML-guided framework of sequential learning for manufacturing process optimization. We apply our methodology to the Rapid Spray Plasma Processing (RSPP) technique for perovskite thin films in ambient conditions. With a limited experimental budget of screening 100 process conditions, we demonstrated an efficiency improvement to 18.5% as the best-in-our-lab device fabricated by RSPP, and we also experimentally found 10 unique process conditions to produce the top-performing devices of more than 17% efficiency, which is 5 times higher rate of success than the control experiments with pseudo-random Latin hypercube sampling. Our model is enabled by three innovations: (a) flexible knowledge transfer between experimental processes by incorporating data from prior experimental data as a probabilistic constraint; (b) incorporation of both subjective human observations and ML insights when selecting next experiments; (c) adaptive strategy of locating the region of interest using Bayesian optimization first, and then conducting local exploration for high-efficiency devices. Furthermore, in virtual benchmarking, our framework achieves faster improvements with limited experimental budgets than traditional design-of-experiments methods (e.g., one-variable-at-a-time sampling).
Recently, there is great interest to investigate the application of deep learning models for the prediction of clinical events using electronic health records (EHR) data. In EHR data, a patient's history is often represented as a sequence of visits, and each visit contains multiple events. As a result, deep learning models developed for sequence modeling, like recurrent neural networks (RNNs) are common architecture for EHR-based clinical events predictive models. While a large variety of RNN models were proposed in the literature, it is unclear if complex architecture innovations will offer superior predictive performance. In order to move this field forward, a rigorous evaluation of various methods is needed. In this study, we conducted a thorough benchmark of RNN architectures in modeling EHR data. We used two prediction tasks: the risk for developing heart failure and the risk of early readmission for inpatient hospitalization. We found that simple gated RNN models, including GRUs and LSTMs, often offer competitive results when properly tuned with Bayesian Optimization, which is in line with similar to findings in the natural language processing (NLP) domain. For reproducibility, Our codebase is shared at https://github.com/ZhiGroup/pytorch_ehr.
Graph Neural Networks (GNNs) can predict the performance of an industrial design quickly and accurately and be used to optimize its shape effectively. However, to fully explore the shape space, one must often consider shapes deviating significantly from the training set. For these, GNN predictions become unreliable, something that is often ignored. For optimization techniques relying on Gaussian Processes, Bayesian Optimization (BO) addresses this issue by exploiting their ability to assess their own accuracy. Unfortunately, this is harder to do when using neural networks because standard approaches to estimating their uncertainty can entail high computational loads and reduced model accuracy. Hence, we propose a novel uncertainty-based method tailored to shape optimization. It enables effective BO and increases the quality of the resulting shapes beyond that of state-of-the-art approaches.
Testing self-driving cars in different areas requires surrounding cars with accordingly different driving styles such as aggressive or conservative styles. A method of numerically measuring and differentiating human driving styles to create a virtual driver with a certain driving style is in demand. However, most methods for measuring human driving styles require thresholds or labels to classify the driving styles, and some require additional questionnaires for drivers about their driving attitude. These limitations are not suitable for creating a large virtual testing environment. Driving models (DMs) simulate human driving styles. Calibrating a DM makes the simulated driving behavior closer to human-driving behavior, and enable the simulation of human-driving cars. Conventional DM-calibrating methods do not take into account that the parameters in a DM vary while driving. These "fixed" calibrating methods cannot reflect an actual interactive driving scenario. In this paper, we propose a DM-calibration method for measuring human driving styles to reproduce real car-following behavior more accurately. The method includes 1) an objective entropy weight method for measuring and clustering human driving styles, and 2) online adaption of DM parameters based on deep learning by combining Bayesian optimization (BO) and a gated recurrent unit neural network. We conducted experiments to evaluate the proposed method, and the results indicate that it can be easily used to measure human driver styles. The experiments also showed that we can calibrate a corresponding DM in a virtual testing environment with up to 26% more accuracy than with fixed calibration methods.
Photon attenuation and scatter are the two main physical factors affecting the diagnostic quality of SPECT in its applications in brain imaging. In this work, we present a novel Bayesian Optimization approach for Attenuation Correction (BOAC) in SPECT brain imaging. BOAC utilizes a prior model parametrizing the head geometry and exploits High Performance Computing (HPC) to reconstruct attenuation corrected images without requiring prior anatomical information from complementary CT scans. BOAC is demonstrated in SPECT brain imaging using noisy and attenuated sinograms, simulated from numerical phantoms. The quality of the tomographic images obtained with the proposed method are compared to those obtained without attenuation correction by employing the appropriate image quality metrics. The quantitative results show the capacity of BOAC to provide images exhibiting higher contrast and less background artifacts as compared to the non-attenuation corrected MLEM images.
Many real world scientific and industrial applications require optimizing multiple competing black-box objectives. When the objectives are expensive-to-evaluate, multi-objective Bayesian optimization (BO) is a popular approach because of its high sample efficiency. However, even with recent methodological advances, most existing multi-objective BO methods perform poorly on search spaces with more than a few dozen parameters and rely on global surrogate models that scale cubically with the number of observations. In this work we propose MORBO, a scalable method for multi-objective BO over high-dimensional search spaces. MORBO identifies diverse globally optimal solutions by performing BO in multiple local regions of the design space in parallel using a coordinated strategy. We show that MORBO significantly advances the state-of-the-art in sample efficiency for several high-dimensional synthetic problems and real world applications, including an optical display design problem and a vehicle design problem with 146 and 222 parameters, respectively. On these problems, where existing BO algorithms fail to scale and perform well, MORBO provides practitioners with order-of-magnitude improvements in sample efficiency over the current approach.
Some response surface functions in complex engineering systems are usually highly nonlinear, unformed, and expensive-to-evaluate. To tackle this challenge, Bayesian optimization, which conducts sequential design via a posterior distribution over the objective function, is a critical method used to find the global optimum of black-box functions. Kernel functions play an important role in shaping the posterior distribution of the estimated function. The widely used kernel function, e.g., radial basis function (RBF), is very vulnerable and susceptible to outliers; the existence of outliers is causing its Gaussian process surrogate model to be sporadic. In this paper, we propose a robust kernel function, Asymmetric Elastic Net Radial Basis Function (AEN-RBF). Its validity as a kernel function and computational complexity are evaluated. When compared to the baseline RBF kernel, we prove theoretically that AEN-RBF can realize smaller mean squared prediction error under mild conditions. The proposed AEN-RBF kernel function can also realize faster convergence to the global optimum. We also show that the AEN-RBF kernel function is less sensitive to outliers, and hence improves the robustness of the corresponding Bayesian optimization with Gaussian processes. Through extensive evaluations carried out on synthetic and real-world optimization problems, we show that AEN-RBF outperforms existing benchmark kernel functions.
Pruning is an effective technique for convolutional neural networks (CNNs) model compression, but it is difficult to find the optimal pruning policy due to the large design space. To improve the usability of pruning, many auto pruning methods have been developed. Recently, Bayesian optimization (BO) has been considered to be a competitive algorithm for auto pruning due to its solid theoretical foundation and high sampling efficiency. However, BO suffers from the curse of dimensionality. The performance of BO deteriorates when pruning deep CNNs, since the dimension of the design spaces increase. We propose a novel clustering algorithm that reduces the dimension of the design space to speed up the searching process. Subsequently, a rollback algorithm is proposed to recover the high-dimensional design space so that higher pruning accuracy can be obtained. We validate our proposed method on ResNet, MobileNetV1, and MobileNetV2 models. Experiments show that the proposed method significantly improves the convergence rate of BO when pruning deep CNNs with no increase in running time. The source code is available at https://github.com/fanhanwei/BOCR.