Bayesian optimization has been successfully applied to optimize black-box functions where the number of evaluations is severely limited. However, in many real-world applications, it is hard or impossible to know in advance which designs are feasible due to some physical or system limitations. These issues lead to an even more challenging problem of optimizing an unknown function with unknown constraints. In this paper, we observe that in such scenarios optimal solution typically lies on the boundary between feasible and infeasible regions of the design space, making it considerably more difficult than that with interior optima. Inspired by this observation, we propose BE-CBO, a new Bayesian optimization method that efficiently explores the boundary between feasible and infeasible designs. To identify the boundary, we learn the constraints with an ensemble of neural networks that outperform the standard Gaussian Processes for capturing complex boundaries. Our method demonstrates superior performance against state-of-the-art methods through comprehensive experiments on synthetic and real-world benchmarks. Code available at: https://github.com/yunshengtian/BE-CBO
The challenge of discovering new molecules with desired properties is crucial in domains like drug discovery and material design. Recent advances in deep learning-based generative methods have shown promise but face the issue of sample efficiency due to the computational expense of evaluating the reward function. This paper proposes a novel algorithm for sample-efficient molecular optimization by distilling a powerful genetic algorithm into deep generative policy using GFlowNets training, the off-policy method for amortized inference. This approach enables the deep generative policy to learn from domain knowledge, which has been explicitly integrated into the genetic algorithm. Our method achieves state-of-the-art performance in the official molecular optimization benchmark, significantly outperforming previous methods. It also demonstrates effectiveness in designing inhibitors against SARS-CoV-2 with substantially fewer reward calls.
Offline model-based optimization seeks to optimize against a learned surrogate model without querying the true oracle objective function during optimization. Such tasks are commonly encountered in protein design, robotics, and clinical medicine where evaluating the oracle function is prohibitively expensive. However, inaccurate surrogate model predictions are frequently encountered along offline optimization trajectories. To address this limitation, we propose generative adversarial model-based optimization using adaptive source critic regularization (aSCR) -- a task- and optimizer- agnostic framework for constraining the optimization trajectory to regions of the design space where the surrogate function is reliable. We propose a computationally tractable algorithm to dynamically adjust the strength of this constraint, and show how leveraging aSCR with standard Bayesian optimization outperforms existing methods on a suite of offline generative design tasks. Our code is available at https://github.com/michael-s-yao/gabo
We study the problem of preferential Bayesian optimization (BO), where we aim to optimize a black-box function with only preference feedback over a pair of candidate solutions. Inspired by the likelihood ratio idea, we construct a confidence set of the black-box function using only the preference feedback. An optimistic algorithm with an efficient computational method is then developed to solve the problem, which enjoys an information-theoretic bound on the total cumulative regret, a first-of-its-kind for preferential BO. This bound further allows us to design a scheme to report an estimated best solution, with a guaranteed convergence rate. Experimental results on sampled instances from Gaussian processes, standard test functions, and a thermal comfort optimization problem all show that our method stably achieves better or competitive performance as compared to the existing state-of-the-art heuristics, which, however, do not have theoretical guarantees on regret bounds or convergence.
Robotic systems are typically composed of various subsystems, such as localization and navigation, each encompassing numerous configurable components (e.g., selecting different planning algorithms). Once an algorithm has been selected for a component, its associated configuration options must be set to the appropriate values. Configuration options across the system stack interact non-trivially. Finding optimal configurations for highly configurable robots to achieve desired performance poses a significant challenge due to the interactions between configuration options across software and hardware that result in an exponentially large and complex configuration space. These challenges are further compounded by the need for transferability between different environments and robotic platforms. Data efficient optimization algorithms (e.g., Bayesian optimization) have been increasingly employed to automate the tuning of configurable parameters in cyber-physical systems. However, such optimization algorithms converge at later stages, often after exhausting the allocated budget (e.g., optimization steps, allotted time) and lacking transferability. This paper proposes CURE -- a method that identifies causally relevant configuration options, enabling the optimization process to operate in a reduced search space, thereby enabling faster optimization of robot performance. CURE abstracts the causal relationships between various configuration options and robot performance objectives by learning a causal model in the source (a low-cost environment such as the Gazebo simulator) and applying the learned knowledge to perform optimization in the target (e.g., Turtlebot 3 physical robot). We demonstrate the effectiveness and transferability of CURE by conducting experiments that involve varying degrees of deployment changes in both physical robots and simulation.
Choosing appropriate hyperparameters plays a crucial role in the success of neural networks as hyper-parameters directly control the behavior and performance of the training algorithms. To obtain efficient tuning, Bayesian optimization methods based on Gaussian process (GP) models are widely used. Despite numerous applications of Bayesian optimization in deep learning, the existing methodologies are developed based on a convenient but restrictive assumption that the tuning parameters are independent of each other. However, tuning parameters with conditional dependence are common in practice. In this paper, we focus on two types of them: branching and nested parameters. Nested parameters refer to those tuning parameters that exist only within a particular setting of another tuning parameter, and a parameter within which other parameters are nested is called a branching parameter. To capture the conditional dependence between branching and nested parameters, a unified Bayesian optimization framework is proposed. The sufficient conditions are rigorously derived to guarantee the validity of the kernel function, and the asymptotic convergence of the proposed optimization framework is proven under the continuum-armed-bandit setting. Based on the new GP model, which accounts for the dependent structure among input variables through a new kernel function, higher prediction accuracy and better optimization efficiency are observed in a series of synthetic simulations and real data applications of neural networks. Sensitivity analysis is also performed to provide insights into how changes in hyperparameter values affect prediction accuracy.
Automation is one of the cornerstones of contemporary material discovery. Bayesian optimization (BO) is an essential part of such workflows, enabling scientists to leverage prior domain knowledge into efficient exploration of a large molecular space. While such prior knowledge can take many forms, there has been significant fanfare around the ancillary scientific knowledge encapsulated in large language models (LLMs). However, existing work thus far has only explored LLMs for heuristic materials searches. Indeed, recent work obtains the uncertainty estimate -- an integral part of BO -- from point-estimated, non-Bayesian LLMs. In this work, we study the question of whether LLMs are actually useful to accelerate principled Bayesian optimization in the molecular space. We take a sober, dispassionate stance in answering this question. This is done by carefully (i) viewing LLMs as fixed feature extractors for standard but principled BO surrogate models and by (ii) leveraging parameter-efficient finetuning methods and Bayesian neural networks to obtain the posterior of the LLM surrogate. Our extensive experiments with real-world chemistry problems show that LLMs can be useful for BO over molecules, but only if they have been pretrained or finetuned with domain-specific data.
Bayesian optimization (BO) offers an elegant approach for efficiently optimizing black-box functions. However, acquisition criteria demand their own challenging inner-optimization, which can induce significant overhead. Many practical BO methods, particularly in high dimension, eschew a formal, continuous optimization of the acquisition function and instead search discretely over a finite set of space-filling candidates. Here, we propose to use candidates which lie on the boundary of the Voronoi tessellation of the current design points, so they are equidistant to two or more of them. We discuss strategies for efficient implementation by directly sampling the Voronoi boundary without explicitly generating the tessellation, thus accommodating large designs in high dimension. On a battery of test problems optimized via Gaussian processes with expected improvement, our proposed approach significantly improves the execution time of a multi-start continuous search without a loss in accuracy.
In the pursuit of novel catalyst development to address pressing environmental concerns and energy demand, conventional design and optimization methods often fall short due to the complexity and vastness of the catalyst parameter space. The advent of Machine Learning (ML) has ushered in a new era in the field of catalyst optimization, offering potential solutions to the shortcomings of traditional techniques. However, existing methods fail to effectively harness the wealth of information contained within the burgeoning body of scientific literature on catalyst synthesis. To address this gap, this study proposes an innovative Artificial Intelligence (AI) workflow that integrates Large Language Models (LLMs), Bayesian optimization, and an active learning loop to expedite and enhance catalyst optimization. Our methodology combines advanced language understanding with robust optimization strategies, effectively translating knowledge extracted from diverse literature into actionable parameters for practical experimentation and optimization. In this article, we demonstrate the application of this AI workflow in the optimization of catalyst synthesis for ammonia production. The results underscore the workflow's ability to streamline the catalyst development process, offering a swift, resource-efficient, and high-precision alternative to conventional methods.
Spanning over two decades, the study of qubits in semiconductors for quantum computing has yielded significant breakthroughs. However, the development of large-scale semiconductor quantum circuits is still limited by challenges in efficiently tuning and operating these circuits. Identifying optimal operating conditions for these qubits is complex, involving the exploration of vast parameter spaces. This presents a real 'needle in the haystack' problem, which, until now, has resisted complete automation due to device variability and fabrication imperfections. In this study, we present the first fully autonomous tuning of a semiconductor qubit, from a grounded device to Rabi oscillations, a clear indication of successful qubit operation. We demonstrate this automation, achieved without human intervention, in a Ge/Si core/shell nanowire device. Our approach integrates deep learning, Bayesian optimization, and computer vision techniques. We expect this automation algorithm to apply to a wide range of semiconductor qubit devices, allowing for statistical studies of qubit quality metrics. As a demonstration of the potential of full automation, we characterise how the Rabi frequency and g-factor depend on barrier gate voltages for one of the qubits found by the algorithm. Twenty years after the initial demonstrations of spin qubit operation, this significant advancement is poised to finally catalyze the operation of large, previously unexplored quantum circuits.
Bayesian optimization (BO) is a powerful approach for optimizing complex and expensive-to-evaluate black-box functions. Its importance is underscored in many applications, notably including hyperparameter tuning, but its efficacy depends on efficiently balancing exploration and exploitation. While there has been substantial progress in BO methods, striking this balance remains a delicate process. In this light, we present LLAMBO, a novel approach that integrates the capabilities of Large Language Models (LLM) within BO. At a high level, we frame the BO problem in natural language, enabling LLMs to iteratively propose and evaluate promising solutions conditioned on historical evaluations. More specifically, we explore how combining contextual understanding, few-shot learning proficiency, and domain knowledge of LLMs can improve model-based BO. Our findings illustrate that LLAMBO is effective at zero-shot warmstarting, and enhances surrogate modeling and candidate sampling, especially in the early stages of search when observations are sparse. Our approach is performed in context and does not require LLM finetuning. Additionally, it is modular by design, allowing individual components to be integrated into existing BO frameworks, or function cohesively as an end-to-end method. We empirically validate LLAMBO's efficacy on the problem of hyperparameter tuning, highlighting strong empirical performance across a range of diverse benchmarks, proprietary, and synthetic tasks.
High-dimensional problems have long been considered the Achilles' heel of Bayesian optimization algorithms. Spurred by the curse of dimensionality, a large collection of algorithms aim to make it more performant in this setting, commonly by imposing various simplifying assumptions on the objective. In this paper, we identify the degeneracies that make vanilla Bayesian optimization poorly suited to high-dimensional tasks, and further show how existing algorithms address these degeneracies through the lens of lowering the model complexity. Moreover, we propose an enhancement to the prior assumptions that are typical to vanilla Bayesian optimization algorithms, which reduces the complexity to manageable levels without imposing structural restrictions on the objective. Our modification - a simple scaling of the Gaussian process lengthscale prior with the dimensionality - reveals that standard Bayesian optimization works drastically better than previously thought in high dimensions, clearly outperforming existing state-of-the-art algorithms on multiple commonly considered real-world high-dimensional tasks.
The rapid growth of automated and autonomous instrumentations brings forth an opportunity for the co-orchestration of multimodal tools, equipped with multiple sequential detection methods, or several characterization tools to explore identical samples. This can be exemplified by the combinatorial libraries that can be explored in multiple locations by multiple tools simultaneously, or downstream characterization in automated synthesis systems. In the co-orchestration approaches, information gained in one modality should accelerate the discovery of other modalities. Correspondingly, the orchestrating agent should select the measurement modality based on the anticipated knowledge gain and measurement cost. Here, we propose and implement a co-orchestration approach for conducting measurements with complex observables such as spectra or images. The method relies on combining dimensionality reduction by variational autoencoders with representation learning for control over the latent space structure, and integrated into iterative workflow via multi-task Gaussian Processes (GP). This approach further allows for the native incorporation of the system's physics via a probabilistic model as a mean function of the GP. We illustrated this method for different modalities of piezoresponse force microscopy and micro-Raman on combinatorial $Sm-BiFeO_3$ library. However, the proposed framework is general and can be extended to multiple measurement modalities and arbitrary dimensionality of measured signals. The analysis code that supports the funding is publicly available at https://github.com/Slautin/2024_Co-orchestration.
We leverage multilevel Monte Carlo (MLMC) to improve the performance of multi-step look-ahead Bayesian optimization (BO) methods that involve nested expectations and maximizations. Often these expectations must be computed by Monte Carlo (MC). The complexity rate of naive MC degrades for nested operations, whereas MLMC is capable of achieving the canonical MC convergence rate for this type of problem, independently of dimension and without any smoothness assumptions. Our theoretical study focuses on the approximation improvements for twoand three-step look-ahead acquisition functions, but, as we discuss, the approach is generalizable in various ways, including beyond the context of BO. Our findings are verified numerically and the benefits of MLMC for BO are illustrated on several benchmark examples. Code is available at https://github.com/Shangda-Yang/MLMCBO .
Maximizing a target variable as an operational objective in a structural causal model is an important problem. Existing Causal Bayesian Optimization~(CBO) methods either rely on hard interventions that alter the causal structure to maximize the reward; or introduce action nodes to endogenous variables so that the data generation mechanisms are adjusted to achieve the objective. In this paper, a novel method is introduced to learn the distribution of exogenous variables, which is typically ignored or marginalized through expectation by existing methods. Exogenous distribution learning improves the approximation accuracy of structural causal models in a surrogate model that is usually trained with limited observational data. Moreover, the learned exogenous distribution extends existing CBO to general causal schemes beyond Additive Noise Models~(ANM). The recovery of exogenous variables allows us to use a more flexible prior for noise or unobserved hidden variables. We develop a new CBO method by leveraging the learned exogenous distribution. Experiments on different datasets and applications show the benefits of our proposed method.
A longstanding belief holds that Bayesian Optimization (BO) with standard Gaussian processes (GP) -- referred to as standard BO -- underperforms in high-dimensional optimization problems. While this belief seems plausible, it lacks both robust empirical evidence and theoretical justification. To address this gap, we present a systematic investigation. First, through a comprehensive evaluation across eleven widely used benchmarks, we found that while the popular Square Exponential (SE) kernel often leads to poor performance, using Matern kernels enables standard BO to consistently achieve top-tier results, frequently surpassing methods specifically designed for high-dimensional optimization. Second, our theoretical analysis reveals that the SE kernels failure primarily stems from improper initialization of the length-scale parameters, which are commonly used in practice but can cause gradient vanishing in training. We provide a probabilistic bound to characterize this issue, showing that Matern kernels are less susceptible and can robustly handle much higher dimensions. Third, we propose a simple robust initialization strategy that dramatically improves the performance of the SE kernel, bringing it close to state of the art methods, without requiring any additional priors or regularization. We prove another probabilistic bound that demonstrates how the gradient vanishing issue can be effectively mitigated with our method. Our findings advocate for a re-evaluation of standard BOs potential in high-dimensional settings.
It is widely known that state-of-the-art machine learning models, including vision and language models, can be seriously compromised by adversarial perturbations. It is therefore increasingly relevant to develop capabilities to certify their performance in the presence of the most effective adversarial attacks. Our paper offers a new approach to certify the performance of machine learning models in the presence of adversarial attacks with population level risk guarantees. In particular, we introduce the notion of $(\alpha,\zeta)$-safe machine learning model. We propose a hypothesis testing procedure, based on the availability of a calibration set, to derive statistical guarantees providing that the probability of declaring that the adversarial (population) risk of a machine learning model is less than $\alpha$ (i.e. the model is safe), while the model is in fact unsafe (i.e. the model adversarial population risk is higher than $\alpha$), is less than $\zeta$. We also propose Bayesian optimization algorithms to determine efficiently whether a machine learning model is $(\alpha,\zeta)$-safe in the presence of an adversarial attack, along with statistical guarantees. We apply our framework to a range of machine learning models - including various sizes of vision Transformer (ViT) and ResNet models - impaired by a variety of adversarial attacks, such as PGDAttack, MomentumAttack, GenAttack and BanditAttack, to illustrate the operation of our approach. Importantly, we show that ViT's are generally more robust to adversarial attacks than ResNets, and large models are generally more robust than smaller models. Our approach goes beyond existing empirical adversarial risk-based certification guarantees. It formulates rigorous (and provable) performance guarantees that can be used to satisfy regulatory requirements mandating the use of state-of-the-art technical tools.
Bayesian Optimization (BO) is an effective method for finding the global optimum of expensive black-box functions. However, it is well known that applying BO to high-dimensional optimization problems is challenging. To address this issue, a promising solution is to use a local search strategy that partitions the search domain into local regions with high likelihood of containing the global optimum, and then use BO to optimize the objective function within these regions. In this paper, we propose a novel technique for defining the local regions using the Covariance Matrix Adaptation (CMA) strategy. Specifically, we use CMA to learn a search distribution that can estimate the probabilities of data points being the global optimum of the objective function. Based on this search distribution, we then define the local regions consisting of data points with high probabilities of being the global optimum. Our approach serves as a meta-algorithm as it can incorporate existing black-box BO optimizers, such as BO, TuRBO, and BAxUS, to find the global optimum of the objective function within our derived local regions. We evaluate our proposed method on various benchmark synthetic and real-world problems. The results demonstrate that our method outperforms existing state-of-the-art techniques.
BayesianOptimization(BO) is a sample-efficient black-box optimizer, and extensive methods have been proposed to build the absolute function response of the black-box function through a probabilistic surrogate model, including Tree-structured Parzen Estimator (TPE), random forest (SMAC), and Gaussian process (GP). However, few methods have been explored to estimate the relative rankings of candidates, which can be more robust to noise and have better practicality than absolute function responses, especially when the function responses are intractable but preferences can be acquired. To this end, we propose a novel ranking-based surrogate model based on the Poisson process and introduce an efficient BO framework, namely Poisson Process Bayesian Optimization (PoPBO). Two tailored acquisition functions are further derived from classic LCB and EI to accommodate it. Compared to the classic GP-BO method, our PoPBO has lower computation costs and better robustness to noise, which is verified by abundant experiments. The results on both simulated and real-world benchmarks, including hyperparameter optimization (HPO) and neural architecture search (NAS), show the effectiveness of PoPBO.
Determining the optimal cost function parameters of Model Predictive Control (MPC) to optimize multiple control objectives is a challenging and time-consuming task. Multiobjective Bayesian Optimization (BO) techniques solve this problem by determining a Pareto optimal parameter set for an MPC with static weights. However, a single parameter set may not deliver the most optimal closed-loop control performance when the context of the MPC operating conditions changes during its operation, urging the need to adapt the cost function weights at runtime. Deep Reinforcement Learning (RL) algorithms can automatically learn context-dependent optimal parameter sets and dynamically adapt for a Weightsvarying MPC (WMPC). However, learning cost function weights from scratch in a continuous action space may lead to unsafe operating states. To solve this, we propose a novel approach limiting the RL actions within a safe learning space representing a catalog of pre-optimized BO Pareto-optimal weight sets. We conceive a RL agent not to learn in a continuous space but to proactively anticipate upcoming control tasks and to choose the most optimal discrete actions, each corresponding to a single set of Pareto optimal weights, context-dependent. Hence, even an untrained RL agent guarantees a safe and optimal performance. Experimental results demonstrate that an untrained RL-WMPC shows Pareto-optimal closed-loop behavior and training the RL-WMPC helps exhibit a performance beyond the Pareto-front.