Scientific optimization problems are usually concerned with balancing multiple competing objectives, which come as preferences over both the outcomes of an experiment (e.g. maximize the reaction yield) and the corresponding input parameters (e.g. minimize the use of an expensive reagent). Typically, practical and economic considerations define a hierarchy over these objectives, which must be reflected in algorithms for sample-efficient experiment planning. Herein, we introduce BoTier, a composite objective that can flexibly represent a hierarchy of preferences over both experiment outcomes and input parameters. We provide systematic benchmarks on synthetic and real-life surfaces, demonstrating the robust applicability of BoTier across a number of use cases. Importantly, BoTier is implemented in an auto-differentiable fashion, enabling seamless integration with the BoTorch library, thereby facilitating adoption by the scientific community.
Existing score-based methods for directed acyclic graph (DAG) learning from observational data struggle to recover the causal graph accurately and sample-efficiently. To overcome this, in this study, we propose DrBO (DAG recovery via Bayesian Optimization)-a novel DAG learning framework leveraging Bayesian optimization (BO) to find high-scoring DAGs. We show that, by sophisticatedly choosing the promising DAGs to explore, we can find higher-scoring ones much more efficiently. To address the scalability issues of conventional BO in DAG learning, we replace Gaussian Processes commonly employed in BO with dropout neural networks, trained in a continual manner, which allows for (i) flexibly modeling the DAG scores without overfitting, (ii) incorporation of uncertainty into the estimated scores, and (iii) scaling with the number of evaluations. As a result, DrBO is computationally efficient and can find the accurate DAG in fewer trials and less time than existing state-of-the-art methods. This is demonstrated through an extensive set of empirical evaluations on many challenging settings with both synthetic and real data. Our implementation is available at https://github.com/baosws/DrBO.
Many important scientific problems involve multivariate optimization coupled with slow and laborious experimental measurements. These complex, high-dimensional searches can be defined by non-convex optimization landscapes that resemble needle-in-a-haystack surfaces, leading to entrapment in local minima. Contextualizing optimizers with human domain knowledge is a powerful approach to guide searches to localized fruitful regions. However, this approach is susceptible to human confirmation bias and it is also challenging for domain experts to keep track of the rapidly expanding scientific literature. Here, we propose the use of Large Language Models (LLMs) for contextualizing Bayesian optimization (BO) via a hybrid optimization framework that intelligently and economically blends stochastic inference with domain knowledge-based insights from the LLM, which is used to suggest new, better-performing areas of the search space for exploration. Our method fosters user engagement by offering real-time commentary on the optimization progress, explaining the reasoning behind the search strategies. We validate the effectiveness of our approach on synthetic benchmarks with up to 15 independent variables and demonstrate the ability of LLMs to reason in four real-world experimental tasks where context-aware suggestions boost optimization performance substantially.
We develop a new methodology to select scenarios of DER adoption most critical for distribution grids. Anticipating risks of future voltage and line flow violations due to additional PV adopters is central for utility investment planning but continues to rely on deterministic or ad hoc scenario selection. We propose a highly efficient search framework based on multi-objective Bayesian Optimization. We treat underlying grid stress metrics as computationally expensive black-box functions, approximated via Gaussian Process surrogates and design an acquisition function based on probability of scenarios being Pareto-critical across a collection of line- and bus-based violation objectives. Our approach provides a statistical guarantee and offers an order of magnitude speed-up relative to a conservative exhaustive search. Case studies on realistic feeders with 200-400 buses demonstrate the effectiveness and accuracy of our approach.
Digital acquisition of bio-signals has been mostly dominated by uniform time sampling following the Nyquist theorem. However, in recent years, new approaches have emerged, focused on sampling a signal only when certain events happen. Currently, the most prominent of these approaches is Level Crossing (LC) sampling. Conventional level crossing analog-to-digital converters (LC-ADC) are often designed to make use of statically defined and uniformly spaced levels. However, a different positioning of the levels, optimized for bio-signals monitoring, can potentially lead to better performing solutions. In this work, we compare multiple LC-level definitions, including statically defined (uniform and logarithmic) configurations and optimization-driven designs (randomized and Bayesian optimization), assessing their ability to maintain signal fidelity while minimizing the sampling rate. In this paper, we analyze the performance of these different methodologies, which is evaluated using the root mean square error (RMSE), the sampling reduction factor (SRF) -- a metric evaluating the sampling compression ratio -- , and error per event metrics to gauge the trade-offs between signal fidelity and data compression. Our findings reveal that optimization-driven LC-sampling, particularly those using Bayesian methods, achieve a lower RMSE without substantially impacting the error per event compared to static configurations, but at the cost of an increase in the sampling rate.
Manual tuning of performance-critical controller parameters can be tedious and sub-optimal. Bayesian Optimization (BO) is an increasingly popular practical alternative to automatically optimize controller parameters from few experiments. Standard BO practice is to evaluate the closed-loop performance of parameters proposed during optimization on an episode with a fixed length. However, fixed-length episodes can be wasteful. For example, continuing an episode where already the start shows undesirable behavior such as strong oscillations seems pointless. Therefore, we propose a BO method that stops an episode early if suboptimality becomes apparent before an episode is completed. Such early stopping results in partial observations of the controller's performance, which cannot directly be included in standard BO. We propose three heuristics to facilitate partially observed episodes in BO. Through five numerical and one hardware experiment, we demonstrate that early stopping BO can substantially reduce the time needed for optimization.
This paper introduces a new approach that leverages Multi-agent Bayesian Optimization (MABO) to design Distributed Model Predictive Control (DMPC) schemes for multi-agent systems. The primary objective is to learn optimal DMPC schemes even when local model predictive controllers rely on imperfect local models. The proposed method invokes a dual decomposition-based distributed optimization framework, incorporating an Alternating Direction Method of Multipliers (ADMM)-based MABO algorithm to enable coordinated learning of parameterized DMPC schemes. This enhances the closed-loop performance of local controllers, despite discrepancies between their models and the actual multi-agent system dynamics. In addition to the newly proposed algorithms, this work also provides rigorous proofs establishing the optimality and convergence of the underlying learning method. Finally, numerical examples are given to demonstrate the efficacy of the proposed MABO-based learning approach.
Modern machine learning algorithms, especially deep learning based techniques, typically involve careful hyperparameter tuning to achieve the best performance. Despite the surge of intense interest in practical techniques like Bayesian optimization and random search based approaches to automating this laborious and compute-intensive task, the fundamental learning theoretic complexity of tuning hyperparameters for deep neural networks is poorly understood. Inspired by this glaring gap, we initiate the formal study of hyperparameter tuning complexity in deep learning through a recently introduced data driven setting. We assume that we have a series of deep learning tasks, and we have to tune hyperparameters to do well on average over the distribution of tasks. A major difficulty is that the utility function as a function of the hyperparameter is very volatile and furthermore, it is given implicitly by an optimization problem over the model parameters. This is unlike previous work in data driven design, where one can typically explicitly model the algorithmic behavior as a function of the hyperparameters. To tackle this challenge, we introduce a new technique to characterize the discontinuities and oscillations of the utility function on any fixed problem instance as we vary the hyperparameter, our analysis relies on subtle concepts including tools from differential/algebraic geometry and constrained optimization. This can be used to show that the learning theoretic complexity of the corresponding family of utility functions is bounded. We instantiate our results and provide sample complexity bounds for concrete applications tuning a hyperparameter that interpolates neural activation functions and setting the kernel parameter in graph neural networks.
A recurring and important task in control engineering is parameter tuning under constraints, which conceptually amounts to optimization of a blackbox function accessible only through noisy evaluations. For example, in control practice parameters of a pre-designed controller are often tuned online in feedback with a plant, and only safe parameter values should be tried, avoiding for example instability. Recently, machine learning methods have been deployed for this important problem, in particular, Bayesian optimization (BO). To handle safety constraints, algorithms from safe BO have been utilized, especially SafeOpt-type algorithms, which enjoy considerable popularity in learning-based control, robotics, and adjacent fields. However, we identify two significant obstacles to practical safety. First, SafeOpt-type algorithms rely on quantitative uncertainty bounds, and most implementations replace these by theoretically unsupported heuristics. Second, the theoretically valid uncertainty bounds crucially depend on a quantity - the reproducing kernel Hilbert space norm of the target function - that at present is impossible to reliably bound using established prior engineering knowledge. By careful numerical experiments we show that these issues can indeed cause safety violations. To overcome these problems, we propose Lipschitz-only Safe Bayesian Optimization (LoSBO), a safe BO algorithm that relies only on a known Lipschitz bound for its safety. Furthermore, we propose a variant (LoS-GP-UCB) that avoids gridding of the search space and is therefore applicable even for moderately high-dimensional problems.
We consider the problem of computing the probability of maximality (PoM) of a Gaussian random vector, i.e., the probability for each dimension to be maximal. This is a key challenge in applications ranging from Bayesian optimization to reinforcement learning, where the PoM not only helps with finding an optimal action, but yields a fine-grained analysis of the action domain, crucial in tasks such as drug discovery. Existing techniques are costly, scaling polynomially in computation and memory with the vector size. We introduce LITE, the first approach for estimating Gaussian PoM with almost-linear time and memory complexity. LITE achieves SOTA accuracy on a number of tasks, while being in practice several orders of magnitude faster than the baselines. This also translates to a better performance on downstream tasks such as entropy estimation and optimal control of bandits. Theoretically, we cast LITE as entropy-regularized UCB and connect it to prior PoM estimators.
Bayesian optimization (BO) is well known to be sample-efficient for solving black-box problems. However, the BO algorithms can sometimes get stuck in suboptimal solutions even with plenty of samples. Intrinsically, such suboptimal problem of BO can attribute to the poor surrogate accuracy of the trained Gaussian process (GP), particularly that in the regions where the optimal solutions locate. Hence, we propose to build multiple GP models instead of a single GP surrogate to complement each other and thus resolving the suboptimal problem of BO. Nevertheless, according to the bias-variance tradeoff equation, the individual prediction errors can increase when increasing the diversity of models, which may lead to even worse overall surrogate accuracy. On the other hand, based on the theory of Rademacher complexity, it has been proved that exploiting the agreement of models on unlabeled information can help to reduce the complexity of the hypothesis space, and therefore achieving the required surrogate accuracy with fewer samples. Such value of model agreement has been extensively demonstrated for co-training style algorithms to boost model accuracy with a small portion of samples. Inspired by the above, we propose a novel BO algorithm labeled as co-learning BO (CLBO), which exploits both model diversity and agreement on unlabeled information to improve the overall surrogate accuracy with limited samples, and therefore achieving more efficient global optimization. Through tests on five numerical toy problems and three engineering benchmarks, the effectiveness of proposed CLBO has been well demonstrated.
Controller tuning is a labor-intensive process that requires human intervention and expert knowledge. Bayesian optimization has been applied successfully in different fields to automate this process. However, when tuning on hardware, such as in automotive applications, strict safety requirements often arise. To obtain safety guarantees, many existing safe Bayesian optimization methods rely on assumptions that are hard to verify in practice. This leads to the use of unjustified heuristics in many applications, which invalidates the theoretical safety guarantees. Furthermore, applications often require multiple safety constraints to be satisfied simultaneously. Building on recently proposed Lipschitz-only safe Bayesian optimization, we develop an algorithm that relies on readily interpretable assumptions and satisfies multiple safety constraints at the same time. We apply this algorithm to the problem of automatically tuning a trajectory-tracking controller of a self-driving car. Results both from simulations and an actual test vehicle underline the algorithm's ability to learn tracking controllers without leaving the track or violating any other safety constraints.
Accurate weather forecasting holds significant importance, serving as a crucial tool for decision-making in various industrial sectors. The limitations of statistical models, assuming independence among data points, highlight the need for advanced methodologies. The correlation between meteorological variables necessitate models capable of capturing complex dependencies. This research highlights the practical efficacy of employing advanced machine learning techniques proposing GenHybQLSTM and BO-QEnsemble architecture based on adaptive weight adjustment strategy. Through comprehensive hyper-parameter optimization using hybrid quantum genetic particle swarm optimisation algorithm and Bayesian Optimization, our model demonstrates a substantial improvement in the accuracy and reliability of meteorological predictions through the assessment of performance metrics such as MSE (Mean Squared Error) and MAPE (Mean Absolute Percentage Prediction Error). The paper highlights the importance of optimized ensemble techniques to improve the performance the given weather forecasting task.
Model predictive control (MPC) controller is considered for temperature management in buildings but its performance heavily depends on hyperparameters. Consequently, MPC necessitates meticulous hyperparameter tuning to attain optimal performance under diverse contracts. However, conventional building controller design is an open-loop process without critical hyperparameter optimization, often leading to suboptimal performance due to unexpected environmental disturbances and modeling errors. Furthermore, these hyperparameters are not adapted to different pricing schemes and may lead to non-economic operations. To address these issues, we propose an efficient performance-oriented building MPC controller tuning method based on a cutting-edge efficient constrained Bayesian optimization algorithm, CONFIG, with global optimality guarantees. We demonstrate that this technique can be applied to efficiently deal with real-world DSM program selection problems under customized black-box constraints and objectives. In this study, a simple MPC controller, which offers the advantages of reduced commissioning costs, enhanced computational efficiency, was optimized to perform on a comparable level to a delicately designed and computationally expensive MPC controller. The results also indicate that with an optimized simple MPC, the monthly electricity cost of a household can be reduced by up to 26.90% compared with the cost when controlled by a basic rule-based controller under the same constraints. Then we compared 12 real electricity contracts in Belgium for a household family with customized black-box occupant comfort constraints. The results indicate a monthly electricity bill saving up to 20.18% when the most economic contract is compared with the worst one, which again illustrates the significance of choosing a proper electricity contract.
Glaucoma is a leading cause of irreversible blindness worldwide, emphasizing the critical need for early detection and intervention. In this paper, we present DeepEyeNet, a novel and comprehensive framework for automated glaucoma detection using retinal fundus images. Our approach integrates advanced image standardization through dynamic thresholding, precise optic disc and cup segmentation via a U-Net model, and comprehensive feature extraction encompassing anatomical and texture-based features. We employ a customized ConvNeXtTiny based Convolutional Neural Network (CNN) classifier, optimized using our Adaptive Genetic Bayesian Optimization (AGBO) algorithm. This proposed AGBO algorithm balances exploration and exploitation in hyperparameter tuning, leading to significant performance improvements. Experimental results on the EyePACS-AIROGS-light-V2 dataset demonstrate that DeepEyeNet achieves a high classification accuracy of 95.84%, which was possible due to the effective optimization provided by the novel AGBO algorithm, outperforming existing methods. The integration of sophisticated image processing techniques, deep learning, and optimized hyperparameter tuning through our proposed AGBO algorithm positions DeepEyeNet as a promising tool for early glaucoma detection in clinical settings.
Expected improvement (EI) is one of the most widely used acquisition functions in Bayesian optimization (BO). Despite its proven success in applications for decades, important open questions remain on the theoretical convergence behaviors and rates for EI. In this paper, we contribute to the convergence theory of EI in three novel and critical areas. First, we consider objective functions that fit under the Gaussian process (GP) prior assumption, whereas existing works mostly focus on functions in the reproducing kernel Hilbert space (RKHS). Second, we establish for the first time the asymptotic error bound and its corresponding rate for GP-EI with noisy observations under the GP prior assumption. Third, by investigating the exploration and exploitation properties of the non-convex EI function, we establish improved error bounds of GP-EI for both the noise-free and noisy cases.
Gaussian process (GP) is arguably one of the most widely used machine learning algorithms in practice. One of its prominent applications is Bayesian optimization (BO). Although the vanilla GP itself is already a powerful tool for BO, it is often beneficial to be able to consider the dependencies of multiple outputs. To do so, Multi-task GP (MTGP) is formulated, but it is not trivial to fully understand the derivations of its formulations and their gradients from the previous literature. This paper serves friendly derivations of the MTGP formulations and their gradients.
With the advancement of serverless computing, running machine learning (ML) inference services over a serverless platform has been advocated, given its labor-free scalability and cost effectiveness. Mixture-of-Experts (MoE) models have been a dominant type of model architectures to enable large models nowadays, with parallel expert networks. Serving large MoE models on serverless computing is potentially beneficial, but has been underexplored due to substantial challenges in handling the skewed expert popularity and scatter-gather communication bottleneck in MoE model execution, for cost-efficient serverless MoE deployment and performance guarantee. We study optimized MoE model deployment and distributed inference serving on a serverless platform, that effectively predict expert selection, pipeline communication with model execution, and minimize the overall billed cost of serving MoE models. Especially, we propose a Bayesian optimization framework with multi-dimensional epsilon-greedy search to learn expert selections and optimal MoE deployment achieving optimal billed cost, including: 1) a Bayesian decision-making method for predicting expert popularity; 2) flexibly pipelined scatter-gather communication; and 3) an optimal model deployment algorithm for distributed MoE serving. Extensive experiments on AWS Lambda show that our designs reduce the billed cost of all MoE layers by at least 75.67% compared to CPU clusters while maintaining satisfactory inference throughput. As compared to LambdaML in serverless computing, our designs achieves 43.41% lower cost with a throughput decrease of at most 18.76%.
Bayesian Optimization (BO) is a sample-efficient black-box optimizer commonly used in search spaces where hyperparameters are independent. However, in many practical AutoML scenarios, there will be dependencies among hyperparameters, forming a conditional search space, which can be partitioned into structurally distinct subspaces. The structure and dimensionality of hyperparameter configurations vary across these subspaces, challenging the application of BO. Some previous BO works have proposed solutions to develop multiple Gaussian Process models in these subspaces. However, these approaches tend to be inefficient as they require a substantial number of observations to guarantee each GP's performance and cannot capture relationships between hyperparameters across different subspaces. To address these issues, this paper proposes a novel approach to model the response surfaces of all subspaces in one, which can model the relationships between hyperparameters elegantly via a self-attention mechanism. Concretely, we design a structure-aware hyperparameter embedding to preserve the structural information. Then, we introduce an attention-based deep feature extractor, capable of projecting configurations with different structures from various subspaces into a unified feature space, where the response surfaces can be formulated using a single standard Gaussian Process. The empirical results on a simulation function, various real-world tasks, and HPO-B benchmark demonstrate that our proposed approach improves the efficacy and efficiency of BO within conditional search spaces.
This research presents a robust approach to classifying COVID-19 cough sounds using cutting-edge machine-learning techniques. Leveraging deep neural decision trees and deep neural decision forests, our methodology demonstrates consistent performance across diverse cough sound datasets. We begin with a comprehensive extraction of features to capture a wide range of audio features from individuals, whether COVID-19 positive or negative. To determine the most important features, we use recursive feature elimination along with cross-validation. Bayesian optimization fine-tunes hyper-parameters of deep neural decision tree and deep neural decision forest models. Additionally, we integrate the SMOTE during training to ensure a balanced representation of positive and negative data. Model performance refinement is achieved through threshold optimization, maximizing the ROC-AUC score. Our approach undergoes a comprehensive evaluation in five datasets: Cambridge, Coswara, COUGHVID, Virufy, and the combined Virufy with the NoCoCoDa dataset. Consistently outperforming state-of-the-art methods, our proposed approach yields notable AUC scores of 0.97, 0.98, 0.92, 0.93, 0.99, and 0.99 across the respective datasets. Merging all datasets into a combined dataset, our method, using a deep neural decision forest classifier, achieves an AUC of 0.97. Also, our study includes a comprehensive cross-datasets analysis, revealing demographic and geographic differences in the cough sounds associated with COVID-19. These differences highlight the challenges in transferring learned features across diverse datasets and underscore the potential benefits of dataset integration, improving generalizability and enhancing COVID-19 detection from audio signals.