Gaussian processes (GPs) are non-parametric probabilistic regression models that are popular due to their flexibility, data efficiency, and well-calibrated uncertainty estimates. However, standard GP models assume homoskedastic Gaussian noise, while many real-world applications are subject to non-Gaussian corruptions. Variants of GPs that are more robust to alternative noise models have been proposed, and entail significant trade-offs between accuracy and robustness, and between computational requirements and theoretical guarantees. In this work, we propose and study a GP model that achieves robustness against sparse outliers by inferring data-point-specific noise levels with a sequential selection procedure maximizing the log marginal likelihood that we refer to as relevance pursuit. We show, surprisingly, that the model can be parameterized such that the associated log marginal likelihood is strongly concave in the data-point-specific noise variances, a property rarely found in either robust regression objectives or GP marginal likelihoods. This in turn implies the weak submodularity of the corresponding subset selection problem, and thereby proves approximation guarantees for the proposed algorithm. We compare the model's performance relative to other approaches on diverse regression and Bayesian optimization tasks, including the challenging but common setting of sparse corruptions of the labels within or close to the function range.
The star tracker is generally affected by the atmospheric background light and the aerodynamic environment when working in near space, which results in missing stars or false stars. Moreover, high-speed maneuvering may cause star trailing, which reduces the accuracy of the star position. To address the challenges for starmap identification, a reverse attitude statistics based method is proposed to handle position noise, false stars, and missing stars. Conversely to existing methods which match before solving for attitude, this method introduces attitude solving into the matching process, and obtains the final match and the correct attitude simultaneously by frequency statistics. Firstly, based on stable angular distance features, the initial matching is obtained by utilizing spatial hash indexing. Then, the dual-vector attitude determination is introduced to calculate potential attitude. Finally, the star pairs are accurately matched by applying a frequency statistics filtering method. In addition, Bayesian optimization is employed to find optimal parameters under the impact of noises, which is able to enhance the algorithm performance further. In this work, the proposed method is validated in simulation, field test and on-orbit experiment. Compared with the state-of-the-art, the identification rate is improved by more than 14.3%, and the solving time is reduced by over 28.5%.
Optimizing black-box functions in high-dimensional search spaces has been known to be challenging for traditional Bayesian Optimization (BO). In this paper, we introduce HiBO, a novel hierarchical algorithm integrating global-level search space partitioning information into the acquisition strategy of a local BO-based optimizer. HiBO employs a search-tree-based global-level navigator to adaptively split the search space into partitions with different sampling potential. The local optimizer then utilizes this global-level information to guide its acquisition strategy towards most promising regions within the search space. A comprehensive set of evaluations demonstrates that HiBO outperforms state-of-the-art methods in high-dimensional synthetic benchmarks and presents significant practical effectiveness in the real-world task of tuning configurations of database management systems (DBMSs).
Bayesian optimization devolves the global optimization of a costly objective function to the global optimization of a sequence of acquisition functions. This inner-loop optimization can be catastrophically difficult if it involves posterior sample paths, especially in higher dimensions. We introduce an efficient global optimization strategy for posterior samples based on global rootfinding. It provides gradient-based optimizers with two sets of judiciously selected starting points, designed to combine exploration and exploitation. The number of starting points can be kept small without sacrificing optimization quality. Remarkably, even with just one point from each set, the global optimum is discovered most of the time. The algorithm scales practically linearly to high dimensions, breaking the curse of dimensionality. For Gaussian process Thompson sampling (GP-TS), we demonstrate remarkable improvement in both inner- and outer-loop optimization, surprisingly outperforming alternatives like EI and GP-UCB in most cases. Our approach also improves the performance of other posterior sample-based acquisition functions, such as variants of entropy search. Furthermore, we propose a sample-average formulation of GP-TS, which has a parameter to explicitly control exploitation and can be computed at the cost of one posterior sample. Our implementation is available at https://github.com/UQUH/TSRoots .
This study investigates the application of Bayesian Optimization (BO) for the hyperparameter tuning of neural networks, specifically targeting the enhancement of Convolutional Neural Networks (CNN) for image classification tasks. Bayesian Optimization is a derivative-free global optimization method suitable for expensive black-box functions with continuous inputs and limited evaluation budgets. The BO algorithm leverages Gaussian Process regression and acquisition functions like Upper Confidence Bound (UCB) and Expected Improvement (EI) to identify optimal configurations effectively. Using the Ax and BOTorch frameworks, this work demonstrates the efficiency of BO in reducing the number of hyperparameter tuning trials while achieving competitive model performance. Experimental outcomes reveal that BO effectively balances exploration and exploitation, converging rapidly towards optimal settings for CNN architectures. This approach underlines the potential of BO in automating neural network tuning, contributing to improved accuracy and computational efficiency in machine learning pipelines.
Radio resource allocation often calls for the optimization of black-box objective functions whose evaluation is expensive in real-world deployments. Conventional optimization methods apply separately to each new system configuration, causing the number of evaluations to be impractical under constraints on computational resources or timeliness. Toward a remedy for this issue, this paper introduces a multi-fidelity continual optimization framework that hinges on a novel information-theoretic acquisition function. The new strategy probes candidate solutions so as to balance the need to retrieve information about the current optimization task with the goal of acquiring information transferable to future resource allocation tasks, while satisfying a query budget constraint. Experiments on uplink power control in a multi-cell multi-antenna system demonstrate that the proposed method substantially improves the optimization efficiency after processing a sufficiently large number of tasks.
This study introduces SLLMBO, an innovative framework leveraging large language models (LLMs) for hyperparameter optimization (HPO), incorporating dynamic search space adaptability, enhanced parameter space exploitation, and a novel LLM-tree-structured parzen estimator (LLM-TPE) sampler. By addressing limitations in recent fully LLM-based methods and traditional bayesian optimization (BO), SLLMBO achieves more robust optimization. This comprehensive benchmarking evaluates multiple LLMs, including GPT-3.5-Turbo, GPT-4o, Claude-Sonnet-3.5, and Gemini-1.5-Flash, extending prior work and establishing SLLMBO as the first framework to benchmark a diverse set of LLMs for HPO. By integrating LLMs' established strengths in parameter initialization with the exploitation abilities demonstrated in this study, alongside TPE's exploration capabilities, the LLM-TPE sampler achieves a balanced exploration-exploitation trade-off, reduces API costs, and mitigates premature early stoppings for more effective parameter searches. Across 14 tabular tasks in classification and regression, the LLM-TPE sampler outperformed fully LLM-based methods and achieved superior results over BO methods in 9 tasks. Testing early stopping in budget-constrained scenarios demonstrated competitive performance, indicating that LLM-based methods generally benefit from extended iterations for optimal results. This work lays the foundation for future research exploring open-source LLMs, reproducibility of LLM results in HPO, and benchmarking SLLMBO on complex datasets, such as image classification, segmentation, and machine translation.
One of the first tasks we learn as children is to grasp objects based on our tactile perception. Incorporating such skill in robots will enable multiple applications, such as increasing flexibility in industrial processes or providing assistance to people with physical disabilities. However, the difficulty lies in adapting the grasping strategies to a large variety of tasks and objects, which can often be unknown. The brute-force solution is to learn new grasps by trial and error, which is inefficient and ineffective. In contrast, Bayesian optimization applies active learning by adding information to the approximation of an optimal grasp. This paper proposes the use of Bayesian optimization techniques to safely perform robotic grasping. We analyze different grasp metrics to provide realistic grasp optimization in a real system including tactile sensors. An experimental evaluation in the robotic system shows the usefulness of the method for performing unknown object grasping even in the presence of noise and uncertainty inherent to a real-world environment.
Bayesian optimization relies on iteratively constructing and optimizing an acquisition function. The latter turns out to be a challenging, non-convex optimization problem itself. Despite the relative importance of this step, most algorithms employ sampling- or gradient-based methods, which do not provably converge to global optima. This work investigates mixed-integer programming (MIP) as a paradigm for \textit{global} acquisition function optimization. Specifically, our Piecewise-linear Kernel Mixed Integer Quadratic Programming (PK-MIQP) formulation introduces a piecewise-linear approximation for Gaussian process kernels and admits a corresponding MIQP representation for acquisition functions. We analyze the theoretical regret bounds of the proposed approximation, and empirically demonstrate the framework on synthetic functions, constrained benchmarks, and a hyperparameter tuning task.
Recommender systems (RS) are pivotal in managing information overload in modern digital services. A key challenge in RS is efficiently processing vast item pools to deliver highly personalized recommendations under strict latency constraints. Multi-stage cascade ranking addresses this by employing computationally efficient retrieval methods to cover diverse user interests, followed by more precise ranking models to refine the results. In the retrieval stage, multi-channel retrieval is often used to generate distinct item subsets from different candidate generators, leveraging the complementary strengths of these methods to maximize coverage. However, forwarding all retrieved items overwhelms downstream rankers, necessitating truncation. Despite advancements in individual retrieval methods, multi-channel fusion, the process of efficiently merging multi-channel retrieval results, remains underexplored. We are the first to identify and systematically investigate multi-channel fusion in the retrieval stage. Current industry practices often rely on heuristic approaches and manual designs, which often lead to suboptimal performance. Moreover, traditional gradient-based methods like SGD are unsuitable for this task due to the non-differentiable nature of the selection process. In this paper, we explore advanced channel fusion strategies by assigning systematically optimized weights to each channel. We utilize black-box optimization techniques, including the Cross Entropy Method and Bayesian Optimization for global weight optimization, alongside policy gradient-based approaches for personalized merging. Our methods enhance both personalization and flexibility, achieving significant performance improvements across multiple datasets and yielding substantial gains in real-world deployments, offering a scalable solution for optimizing multi-channel fusion in retrieval.
Metastatic prostate cancer is one of the leading causes of cancer-related morbidity and mortality worldwide. It is characterized by a high mortality rate and a poor prognosis. In this work, we explore how a clinical oncologist can apply a Stackelberg game-theoretic framework to prolong metastatic prostate cancer survival, or even make it chronic in duration. We utilize a Bayesian optimization approach to identify the optimal adaptive chemotherapeutic treatment policy for a single drug (Abiraterone) to maximize the time before the patient begins to show symptoms. We show that, with precise adaptive optimization of drug delivery, it is possible to significantly prolong the cancer suppression period, potentially converting metastatic prostate cancer from a terminal disease to a chronic disease for most patients, as supported by clinical and analytical evidence. We suggest that clinicians might explore the possibility of implementing a high-level tight control (HLTC) treatment, in which the trigger signals (i.e. biomarker levels) for drug administration and cessation are both high and close together, typically yield the best outcomes, as demonstrated through both computation and theoretical analysis. This simple insight could serve as a valuable guide for improving current adaptive chemotherapy treatments in other hormone-sensitive cancers.
This research proposes a framework for modeling and comparing two electricity scenarios for Nigeria by 2050, focusing on the inclusion and exclusion of electricity storage technologies. A Central Composite Design (CCD) was used to generate a design matrix for data collection, with EnergyPLAN software used to create energy system simulations on the CCD data for four outputs: total annual cost, CO2 emissions, critical excess electricity production (CEEP), and electricity import. Three machine learning algorithms, support vector regression (SVR), extreme gradient boosting (XGBoost), and multi-layer perceptron (MLP), were tuned using Bayesian optimization to develop models mapping the inputs to outputs. A genetic algorithm was employed for multi-objective optimization to determine the optimal input capacities that minimize the outputs. Results indicated that incorporating electricity storage technologies (EST) leads to a 37% increase in renewable electricity sources (RES) share, resulting in a 19.14% reduction in CO2 emissions. EST such as battery energy storage systems (BESS), pumped hydro storage (PHS), and vehicle-to-grid (V2G) storage allow for the storage of the critical excess electricity that comes with increasing RES share. Integrating EST in Nigeria's 2050 energy landscape is crucial for incorporating more renewable electricity sources into the energy system, thereby reducing CO2 emissions and managing excess electricity production. This study outlines a plan for optimal electricity production to meet Nigeria's 2050 demand, highlighting the need for a balanced approach that combines fossil fuels, renewable energy, nuclear power, and advanced storage solutions to achieve a sustainable and efficient electricity system.
Amortized meta-learning methods based on pre-training have propelled fields like natural language processing and vision. Transformer-based neural processes and their variants are leading models for probabilistic meta-learning with a tractable objective. Often trained on synthetic data, these models implicitly capture essential latent information in the data-generation process. However, existing methods do not allow users to flexibly inject (condition on) and extract (predict) this probabilistic latent information at runtime, which is key to many tasks. We introduce the Amortized Conditioning Engine (ACE), a new transformer-based meta-learning model that explicitly represents latent variables of interest. ACE affords conditioning on both observed data and interpretable latent variables, the inclusion of priors at runtime, and outputs predictive distributions for discrete and continuous data and latents. We show ACE's modeling flexibility and performance in diverse tasks such as image completion and classification, Bayesian optimization, and simulation-based inference.
Accurate forecasting of electrical demand is essential for maintaining a stable and reliable power grid, optimizing the allocation of energy resources, and promoting efficient energy consumption practices. This study investigates the effectiveness of five hyperparameter optimization (HPO) algorithms -- Random Search, Covariance Matrix Adaptation Evolution Strategy (CMA--ES), Bayesian Optimization, Partial Swarm Optimization (PSO), and Nevergrad Optimizer (NGOpt) across univariate and multivariate Short-Term Load Forecasting (STLF) tasks. Using the Panama Electricity dataset (n=48,049), we evaluate HPO algorithms' performances on a surrogate forecasting algorithm, XGBoost, in terms of accuracy (i.e., MAPE, $R^2$) and runtime. Performance plots visualize these metrics across varying sample sizes from 1,000 to 20,000, and Kruskal--Wallis tests assess the statistical significance of the performance differences. Results reveal significant runtime advantages for HPO algorithms over Random Search. In univariate models, Bayesian optimization exhibited the lowest accuracy among the tested methods. This study provides valuable insights for optimizing XGBoost in the STLF context and identifies areas for future research.
This paper studies a non-stationary kernelized bandit (KB) problem, also called time-varying Bayesian optimization, where one seeks to minimize the regret under an unknown reward function that varies over time. In particular, we focus on a near-optimal algorithm whose regret upper bound matches the regret lower bound. For this goal, we show the first algorithm-independent regret lower bound for non-stationary KB with squared exponential and Mat\'ern kernels, which reveals that an existing optimization-based KB algorithm with slight modification is near-optimal. However, this existing algorithm suffers from feasibility issues due to its huge computational cost. Therefore, we propose a novel near-optimal algorithm called restarting phased elimination with random permutation (R-PERP), which bypasses the huge computational cost. A technical key point is the simple permutation procedures of query candidates, which enable us to derive a novel tighter confidence bound tailored to the non-stationary problems.
In Bayesian optimization, a black-box function is maximized via the use of a surrogate model. We apply distributed Thompson sampling, using a Gaussian process as a surrogate model, to approach the multi-agent Bayesian optimization problem. In our distributed Thompson sampling implementation, each agent receives sampled points from neighbors, where the communication network is encoded in a graph; each agent utilizes their own Gaussian process to model the objective function. We demonstrate theoretical bounds on Bayesian average regret and Bayesian simple regret, where the bound depends on the structure of the communication graph. Unlike in batch Bayesian optimization, this bound is applicable in cases where the communication graph amongst agents is constrained. When compared to sequential single-agent Thompson sampling, our bound guarantees faster convergence with respect to time as long as the communication graph is connected. We confirm the efficacy of our algorithm with numerical simulations on traditional optimization test functions, demonstrating the significance of graph connectivity on improving regret convergence.
This paper introduces a framework for Bayesian Optimization (BO) with metric movement costs, addressing a critical challenge in practical applications where input alterations incur varying costs. Our approach is a convenient plug-in that seamlessly integrates with the existing literature on batched algorithms, where designs within batches are observed following the solution of a Traveling Salesman Problem. The proposed method provides a theoretical guarantee of convergence in terms of movement costs for BO. Empirically, our method effectively reduces average movement costs over time while maintaining comparable regret performance to conventional BO methods. This framework also shows promise for broader applications in various bandit settings with movement costs.
Acute lymphoblastic leukemia (ALL) is the most malignant form of leukemia and the most common cancer in adults and children. Traditionally, leukemia is diagnosed by analyzing blood and bone marrow smears under a microscope, with additional cytochemical tests for confirmation. However, these methods are expensive, time consuming, and highly dependent on expert knowledge. In recent years, deep learning, particularly Convolutional Neural Networks (CNNs), has provided advanced methods for classifying microscopic smear images, aiding in the detection of leukemic cells. These approaches are quick, cost effective, and not subject to human bias. However, most methods lack the ability to quantify uncertainty, which could lead to critical misdiagnoses. In this research, hybrid deep learning models (InceptionV3-GRU, EfficientNetB3-GRU, MobileNetV2-GRU) were implemented to classify ALL. Bayesian optimization was used to fine tune the model's hyperparameters and improve its performance. Additionally, Deep Ensemble uncertainty quantification was applied to address uncertainty during leukemia image classification. The proposed models were trained on the publicly available datasets ALL-IDB1 and ALL-IDB2. Their results were then aggregated at the score level using the sum rule. The parallel architecture used in these models offers a high level of confidence in differentiating between ALL and non-ALL cases. The proposed method achieved a remarkable detection accuracy rate of 100% on the ALL-IDB1 dataset, 98.07% on the ALL-IDB2 dataset, and 98.64% on the combined dataset, demonstrating its potential for accurate and reliable leukemia diagnosis.
Bayesian Optimization (BO) is widely used for optimising black-box functions but requires us to specify the length scale hyperparameter, which defines the smoothness of the functions the optimizer will consider. Most current BO algorithms choose this hyperparameter by maximizing the marginal likelihood of the observed data, albeit risking misspecification if the objective function is less smooth in regions we have not yet explored. The only prior solution addressing this problem with theoretical guarantees was A-GP-UCB, proposed by Berkenkamp et al. (2019). This algorithm progressively decreases the length scale, expanding the class of functions considered by the optimizer. However, A-GP-UCB lacks a stopping mechanism, leading to over-exploration and slow convergence. To overcome this, we introduce Length scale Balancing (LB) - a novel approach, aggregating multiple base surrogate models with varying length scales. LB intermittently adds smaller length scale candidate values while retaining longer scales, balancing exploration and exploitation. We formally derive a cumulative regret bound of LB and compare it with the regret of an oracle BO algorithm using the optimal length scale. Denoting the factor by which the regret bound of A-GP-UCB was away from oracle as $g(T)$, we show that LB is only $\log g(T)$ away from oracle regret. We also empirically evaluate our algorithm on synthetic and real-world benchmarks and show it outperforms A-GP-UCB, maximum likelihood estimation and MCMC.
Bayesian optimization (BO) has become an indispensable tool for autonomous decision-making across diverse applications from autonomous vehicle control to accelerated drug and materials discovery. With the growing interest in self-driving laboratories, BO of chemical systems is crucial for machine learning (ML) guided experimental planning. Typically, BO employs a regression surrogate model to predict the distribution of unseen parts of the search space. However, for the selection of molecules, picking the top candidates with respect to a distribution, the relative ordering of their properties may be more important than their exact values. In this paper, we introduce Rank-based Bayesian Optimization (RBO), which utilizes a ranking model as the surrogate. We present a comprehensive investigation of RBO's optimization performance compared to conventional BO on various chemical datasets. Our results demonstrate similar or improved optimization performance using ranking models, particularly for datasets with rough structure-property landscapes and activity cliffs. Furthermore, we observe a high correlation between the surrogate ranking ability and BO performance, and this ability is maintained even at early iterations of BO optimization when using ranking surrogate models. We conclude that RBO is an effective alternative to regression-based BO, especially for optimizing novel chemical compounds.