Recent work reported that simple Bayesian optimization methods perform well for high-dimensional real-world tasks, seemingly contradicting prior work and tribal knowledge. This paper investigates the 'why'. We identify fundamental challenges that arise in high-dimensional Bayesian optimization and explain why recent methods succeed. Our analysis shows that vanishing gradients caused by Gaussian process initialization schemes play a major role in the failures of high-dimensional Bayesian optimization and that methods that promote local search behaviors are better suited for the task. We find that maximum likelihood estimation of Gaussian process length scales suffices for state-of-the-art performance. Based on this, we propose a simple variant of maximum likelihood estimation called MSR that leverages these findings to achieve state-of-the-art performance on a comprehensive set of real-world applications. We also present targeted experiments to illustrate and confirm our findings.
The traditional heat-load generation pattern of combined heat and power generators has become a problem leading to renewable energy source (RES) power curtailment in cold regions, motivating the proposal of a planning model for alternative heat sources. The model aims to identify non-dominant capacity allocation schemes for heat pumps, thermal energy storage, electric boilers, and combined storage heaters to construct a Pareto front, considering both economic and sustainable objectives. The integration of various heat sources from both generation and consumption sides enhances flexibility in utilization. The study introduces a novel optimization algorithm, the adaptive multi-objective Bayesian optimization (AMBO). Compared to other widely used multi-objective optimization algorithms, AMBO eliminates predefined parameters that may introduce subjectivity from planners. Beyond the algorithm, the proposed model incorporates a noise term to account for inevitable simulation deviations, enabling the identification of better-performing planning results that meet the unique requirements of cold regions. What's more, the characteristics of electric-thermal coupling scenarios are captured and reflected in the operation simulation model to make sure the simulation is close to reality. Numerical simulation verifies the superiority of the proposed approach in generating a more diverse and evenly distributed Pareto front in a sample-efficient manner, providing comprehensive and objective planning choices.
Incorporating user preferences into multi-objective Bayesian optimization (MOBO) allows for personalization of the optimization procedure. Preferences are often abstracted in the form of an unknown utility function, estimated through pairwise comparisons of potential outcomes. However, utility-driven MOBO methods can yield solutions that are dominated by nearby solutions, as non-dominance is not enforced. Additionally, classical MOBO commonly relies on estimating the entire Pareto-front to identify the Pareto-optimal solutions, which can be expensive and ignore user preferences. Here, we present a new method, termed preference-utility-balanced MOBO (PUB-MOBO), that allows users to disambiguate between near-Pareto candidate solutions. PUB-MOBO combines utility-based MOBO with local multi-gradient descent to refine user-preferred solutions to be near-Pareto-optimal. To this end, we propose a novel preference-dominated utility function that concurrently preserves user-preferences and dominance amongst candidate solutions. A key advantage of PUB-MOBO is that the local search is restricted to a (small) region of the Pareto-front directed by user preferences, alleviating the need to estimate the entire Pareto-front. PUB-MOBO is tested on three synthetic benchmark problems: DTLZ1, DTLZ2 and DH1, as well as on three real-world problems: Vehicle Safety, Conceptual Marine Design, and Car Side Impact. PUB-MOBO consistently outperforms state-of-the-art competitors in terms of proximity to the Pareto-front and utility regret across all the problems.
Several scenarios require the optimization of non-convex black-box functions, that are noisy expensive to evaluate functions with unknown analytical expression, whose gradients are hence not accessible. For example, the hyper-parameter tuning problem of machine learning models. Bayesian optimization is a class of methods with state-of-the-art performance delivering a solution to this problem in real scenarios. It uses an iterative process that employs a probabilistic surrogate model, typically a Gaussian process, of the objective function to be optimized computing a posterior predictive distribution of the black-box function. Based on the information given by this posterior predictive distribution, Bayesian optimization includes the computation of an acquisition function that represents, for every input space point, the utility of evaluating that point in the next iteraiton if the objective of the process is to retrieve a global extremum. This paper is a survey of the information theoretical acquisition functions, whose performance typically outperforms the rest of acquisition functions. The main concepts of the field of information theory are also described in detail to make the reader aware of why information theory acquisition functions deliver great results in Bayesian optimization and how can we approximate them when they are intractable. We also cover how information theory acquisition functions can be adapted to complex optimization scenarios such as the multi-objective, constrained, non-myopic, multi-fidelity, parallel and asynchronous settings and provide further lines of research.
Bayesian optimization is highly effective for optimizing expensive-to-evaluate black-box functions, but it faces significant computational challenges due to the high computational complexity of Gaussian processes, which results in a total time complexity that is quartic with respect to the number of iterations. To address this limitation, we propose the Bayesian Optimization by Kernel regression and density-based Exploration (BOKE) algorithm. BOKE uses kernel regression for efficient function approximation, kernel density for exploration, and integrates them into the confidence bound criteria to guide the optimization process, thus reducing computational costs to quadratic. Our theoretical analysis rigorously establishes the global convergence of BOKE and ensures its robustness in noisy settings. Through extensive numerical experiments on both synthetic and real-world optimization tasks, we demonstrate that BOKE not only performs competitively compared to Gaussian process-based methods but also exhibits superior computational efficiency. These results highlight BOKE's effectiveness in resource-constrained environments, providing a practical approach for optimization problems in engineering applications.
Bayesian optimization (BO) has emerged as a powerful tool for guiding experimental design and decision- making in various scientific fields, including materials science, chemistry, and biology. However, despite its growing popularity, the complexity of existing BO libraries and the steep learning curve associated with them can deter researchers who are not well-versed in machine learning or programming. To address this barrier, we introduce Honegumi, a user-friendly, interactive tool designed to simplify the process of creating advanced Bayesian optimization scripts. Honegumi offers a dynamic selection grid that allows users to configure key parameters of their optimization tasks, generating ready-to-use, unit-tested Python scripts tailored to their specific needs. Accompanying the interface is a comprehensive suite of tutorials that provide both conceptual and practical guidance, bridging the gap between theoretical understanding and practical implementation. Built on top of the Ax platform, Honegumi leverages the power of existing state-of-the-art libraries while restructuring the user experience to make advanced BO techniques more accessible to experimental researchers. By lowering the barrier to entry and providing educational resources, Honegumi aims to accelerate the adoption of advanced Bayesian optimization methods across various domains.
The hydro-mechanical behavior of clay-sulfate rocks, especially their swelling properties, poses significant challenges in geotechnical engineering. This study presents a hybrid constrained machine learning (ML) model developed using the categorical boosting algorithm (CatBoost) tuned with a Bayesian optimization algorithm to predict and analyze the swelling behavior of these complex geological materials. Initially, a coupled hydro-mechanical model based on the Richards' equation coupled to a deformation process with linear kinematics implemented within the finite element framework OpenGeoSys was used to simulate the observed ground heave in Staufen, Germany, caused by water inflow into the clay-sulfate bearing Triassic Grabfeld Formation. A systematic parametric analysis using Gaussian distributions of key parameters, including Young's modulus, Poisson's ratio, maximum swelling pressure, permeability, and air entry pressure, was performed to construct a synthetic database. The ML model takes time, spatial coordinates, and these parameter values as inputs, while water saturation, porosity, and vertical displacement are outputs. In addition, penalty terms were incorporated into the CatBoost objective function to enforce physically meaningful predictions. Results show that the hybrid approach effectively captures the nonlinear and dynamic interactions that govern hydro-mechanical processes. The study demonstrates the ability of the model to predict the swelling behavior of clay-sulfate rocks, providing a robust tool for risk assessment and management in affected regions. The results highlight the potential of ML-driven models to address complex geotechnical challenges.
We introduce Social Bayesian Optimization (SBO), a vote-efficient algorithm for consensus-building in collective decision-making. In contrast to single-agent scenarios, collective decision-making encompasses group dynamics that may distort agents' preference feedback, thereby impeding their capacity to achieve a social-influence-free consensus -- the most preferable decision based on the aggregated agent utilities. We demonstrate that under mild rationality axioms, reaching social-influence-free consensus using noisy feedback alone is impossible. To address this, SBO employs a dual voting system: cheap but noisy public votes (e.g., show of hands in a meeting), and more accurate, though expensive, private votes (e.g., one-to-one interview). We model social influence using an unknown social graph and leverage the dual voting system to efficiently learn this graph. Our theoretical findigns show that social graph estimation converges faster than the black-box estimation of agents' utilities, allowing us to reduce reliance on costly private votes early in the process. This enables efficient consensus-building primarily through noisy public votes, which are debiased based on the estimated social graph to infer social-influence-free feedback. We validate the efficacy of SBO across multiple real-world applications, including thermal comfort, team building, travel negotiation, and energy trading collaboration.
This paper presents a unified framework for codifying and automating optimization strategies to efficiently deploy deep neural networks (DNNs) on resource-constrained hardware, such as FPGAs, while maintaining high performance, accuracy, and resource efficiency. Deploying DNNs on such platforms involves addressing the significant challenge of balancing performance, resource usage (e.g., DSPs and LUTs), and inference accuracy, which often requires extensive manual effort and domain expertise. Our novel approach addresses two core key issues: (i)~encoding custom optimization strategies and (ii)~enabling cross-stage optimization search. In particular, our proposed framework seamlessly integrates programmatic DNN optimization techniques with high-level synthesis (HLS)-based metaprogramming, leveraging advanced design space exploration (DSE) strategies like Bayesian optimization to automate both top-down and bottom-up design flows. Hence, we reduce the need for manual intervention and domain expertise. In addition, the framework introduces customizable optimization, transformation, and control blocks to enhance DNN accelerator performance and resource efficiency. Experimental results demonstrate up to a 92\% DSP and 89\% LUT usage reduction for select networks, while preserving accuracy, along with a 15.6-fold reduction in optimization time compared to grid search. These results highlight the potential for automating the generation of resource-efficient DNN accelerator designs with minimum effort.
Accelerated discovery in materials science demands autonomous systems capable of dynamically formulating and solving design problems. In this work, we introduce a novel framework that leverages Bayesian optimization over a problem formulation space to identify optimal design formulations in line with decision-maker preferences. By mapping various design scenarios to a multi attribute utility function, our approach enables the system to balance conflicting objectives such as ductility, yield strength, density, and solidification range without requiring an exact problem definition at the outset. We demonstrate the efficacy of our method through an in silico case study on a Mo-Nb-Ti-V-W alloy system targeted for gas turbine engine blade applications. The framework converges on a sweet spot that satisfies critical performance thresholds, illustrating that integrating problem formulation discovery into the autonomous design loop can significantly streamline the experimental process. Future work will incorporate human feedback to further enhance the adaptability of the system in real-world experimental settings.
Large language models (LLMs) have recently been employed as agents to solve sequential decision-making tasks such as Bayesian optimization and multi-armed bandits (MAB). These works usually adopt an LLM for sequential action selection by providing it with a fixed, manually designed meta-prompt. However, numerous previous works have found that the prompt has a significant impact on the performance of the LLM, which calls for a method to automatically optimize the meta-prompt for LLM-based agents. Unfortunately, the non-stationarity in the reward observations during LLM-based sequential decision-making makes meta-prompt optimization highly challenging. To address this challenge, we draw inspirations from adversarial bandit algorithms, which are inherently capable of handling non-stationary reward observations. Building on this foundation, we propose our EXPonential-weight algorithm for prompt Optimization} (EXPO) to automatically optimize the task description and meta-instruction in the meta-prompt for LLM-based agents. We also extend EXPO to additionally optimize the exemplars (i.e., history of interactions) in the meta-prompt to further enhance the performance, hence introducing our EXPO-ES algorithm. We use extensive experiments to show that our algorithms significantly improve the performance of LLM-based sequential decision-making.
The design of analog circuits is a cornerstone of integrated circuit (IC) development, requiring the optimization of complex, interconnected sub-structures such as amplifiers, comparators, and buffers. Traditionally, this process relies heavily on expert human knowledge to refine design objectives by carefully tuning sub-components while accounting for their interdependencies. Existing methods, such as Bayesian Optimization (BO), offer a mathematically driven approach for efficiently navigating large design spaces. However, these methods fall short in two critical areas compared to human expertise: (i) they lack the semantic understanding of the sizing solution space and its direct correlation with design objectives before optimization, and (ii) they fail to reuse knowledge gained from optimizing similar sub-structures across different circuits. To overcome these limitations, we propose the Large Language Model-based Universal Sizing Optimizer (LLM-USO), which introduces a novel method for knowledge representation to encode circuit design knowledge in a structured text format. This representation enables the systematic reuse of optimization insights for circuits with similar sub-structures. LLM-USO employs a hybrid framework that integrates BO with large language models (LLMs) and a learning summary module. This approach serves to: (i) infuse domain-specific knowledge into the BO process and (ii) facilitate knowledge transfer across circuits, mirroring the cognitive strategies of expert designers. Specifically, LLM-USO constructs a knowledge summary mechanism to distill and apply design insights from one circuit to related ones. It also incorporates a knowledge summary critiquing mechanism to ensure the accuracy and quality of the summaries and employs BO-guided suggestion filtering to identify optimal design points efficiently.
Bilevel optimization is characterized by a two-level optimization structure, where the upper-level problem is constrained by optimal lower-level solutions, and such structures are prevalent in real-world problems. The constraint by optimal lower-level solutions poses significant challenges, especially in noisy, constrained, and derivative-free settings, as repeating lower-level optimizations is sample inefficient and predicted lower-level solutions may be suboptimal. We present BILevel Bayesian Optimization (BILBO), a novel Bayesian optimization algorithm for general bilevel problems with blackbox functions, which optimizes both upper- and lower-level problems simultaneously, without the repeated lower-level optimization required by existing methods. BILBO samples from confidence-bounds based trusted sets, which bounds the suboptimality on the lower level. Moreover, BILBO selects only one function query per iteration, where the function query selection strategy incorporates the uncertainty of estimated lower-level solutions and includes a conditional reassignment of the query to encourage exploration of the lower-level objective. The performance of BILBO is theoretically guaranteed with a sublinear regret bound for commonly used kernels and is empirically evaluated on several synthetic and real-world problems.
Time-Varying Bayesian Optimization (TVBO) is the go-to framework for optimizing a time-varying, expensive, noisy black-box function. However, most of the solutions proposed so far either rely on unrealistic assumptions on the nature of the objective function or do not offer any theoretical guarantees. We propose the first analysis that asymptotically bounds the cumulative regret of TVBO algorithms under mild and realistic assumptions only. In particular, we provide an algorithm-independent lower regret bound and an upper regret bound that holds for a large class of TVBO algorithms. Based on this analysis, we formulate recommendations for TVBO algorithms and show how an algorithm (BOLT) that follows them performs better than the state-of-the-art of TVBO through experiments on synthetic and real-world problems.
Many real-world black-box optimization problems have multiple conflicting objectives. Rather than attempting to approximate the entire set of Pareto-optimal solutions, interactive preference learning allows to focus the search on the most relevant subset. However, few previous studies have exploited the fact that utility functions are usually monotonic. In this paper, we address the Bayesian Optimization with Preference Exploration (BOPE) problem and propose using a neural network ensemble as a utility surrogate model. This approach naturally integrates monotonicity and supports pairwise comparison data. Our experiments demonstrate that the proposed method outperforms state-of-the-art approaches and exhibits robustness to noise in utility evaluations. An ablation study highlights the critical role of monotonicity in enhancing performance.
Bayesian optimization is a widely used method for optimizing expensive black-box functions, with Expected Improvement being one of the most commonly used acquisition functions. In contrast, information-theoretic acquisition functions aim to reduce uncertainty about the function's optimum and are often considered fundamentally distinct from EI. In this work, we challenge this prevailing perspective by introducing a unified theoretical framework, Variational Entropy Search, which reveals that EI and information-theoretic acquisition functions are more closely related than previously recognized. We demonstrate that EI can be interpreted as a variational inference approximation of the popular information-theoretic acquisition function, named Max-value Entropy Search. Building on this insight, we propose VES-Gamma, a novel acquisition function that balances the strengths of EI and MES. Extensive empirical evaluations across both low- and high-dimensional synthetic and real-world benchmarks demonstrate that VES-Gamma is competitive with state-of-the-art acquisition functions and in many cases outperforms EI and MES.
In multi-objective black-box optimization, the goal is typically to find solutions that optimize a set of $T$ black-box objective functions, $f_1$, ..., $f_T$, simultaneously. Traditional approaches often seek a single Pareto-optimal set that balances trade-offs among all objectives. In this work, we consider a problem setting that departs from this paradigm: finding a small set of K < T solutions, that collectively "covers" the T objectives. A set of solutions is defined as "covering" if, for each objective $f_1$, ..., $f_T$, there is at least one good solution. A motivating example for this problem setting occurs in drug design. For example, we may have T pathogens and aim to identify a set of K < T antibiotics such that at least one antibiotic can be used to treat each pathogen. To address this problem, we propose Multi-Objective Coverage Bayesian Optimization (MOCOBO), a principled algorithm designed to efficiently find a covering set. We validate our approach through experiments on challenging high-dimensional tasks, including applications in peptide and molecular design, where MOCOBO is shown to find high-performing covering sets of solutions. The results show that the coverage of the K < T solutions found by MOCOBO matches or nearly matches the coverage of T solutions obtained by optimizing each objective individually. Furthermore, in in vitro experiments, the peptides found by MOCOBO exhibited high potency against drug-resistant pathogens, further demonstrating the potential of MOCOBO for drug discovery.
This study considers multi-objective Bayesian optimization (MOBO) through the information gain of the Pareto-frontier. To calculate the information gain, a predictive distribution conditioned on the Pareto-frontier plays a key role, which is defined as a distribution truncated by the Pareto-frontier. However, it is usually impossible to obtain the entire Pareto-frontier in a continuous domain, and therefore, the complete truncation cannot be known. We consider an approximation of the truncate distribution by using a mixture distribution consisting of two possible approximate truncation obtainable from a subset of the Pareto-frontier, which we call over- and under-truncation. Since the optimal balance of the mixture is unknown beforehand, we propose optimizing the balancing coefficient through the variational lower bound maximization framework, by which the approximation error of the information gain can be minimized. Our empirical evaluation demonstrates the effectiveness of the proposed method particularly when the number of objective functions is large.
Variational Quantum Eigensolvers (VQEs) are a powerful class of hybrid quantum-classical algorithms designed to approximate the ground state of a quantum system described by its Hamiltonian. VQEs hold promise for various applications, including lattice field theory. However, the inherent noise of Noisy Intermediate-Scale Quantum (NISQ) devices poses a significant challenge for running VQEs as these algorithms are particularly susceptible to noise, e.g., measurement shot noise and hardware noise. In a recent work, it was proposed to enhance the classical optimization of VQEs with Gaussian Processes (GPs) and Bayesian Optimization, as these machine-learning techniques are well-suited for handling noisy data. In these proceedings, we provide additional insights into this new algorithm and present further numerical experiments. In particular, we examine the impact of hardware noise and error mitigation on the algorithm's performance. We validate the algorithm using classical simulations of quantum hardware, including hardware noise benchmarks, which have not been considered in previous works. Our numerical experiments demonstrate that GP-enhanced algorithms can outperform state-of-the-art baselines, laying the foundation for future research on deploying these techniques to real quantum hardware and lattice field theory setups.
Face detection is a computer vision application that increasingly demands lightweight models to facilitate deployment on devices with limited computational resources. Neural network pruning is a promising technique that can effectively reduce network size without significantly affecting performance. In this work, we propose a novel face detection pruning pipeline that leverages Filter Pruning via Geometric Median (FPGM) pruning, Soft Filter Pruning (SFP) and Bayesian optimization in order to achieve a superior trade-off between size and performance compared to existing approaches. FPGM pruning is a structured pruning technique that allows pruning the least significant filters in each layer, while SFP iteratively prunes the filters and allows them to be updated in any subsequent training step. Bayesian optimization is employed in order to optimize the pruning rates of each layer, rather than relying on engineering expertise to determine the optimal pruning rates for each layer. In our experiments across all three subsets of the WIDER FACE dataset, our proposed approach B-FPGM consistently outperforms existing ones in balancing model size and performance. All our experiments were applied to EResFD, the currently smallest (in number of parameters) well-performing face detector of the literature; a small ablation study with a second small face detector, EXTD, is also reported. The source code and trained pruned face detection models can be found at: https://github.com/IDTITI/B-FPGM.