Bayesian optimization (BO) is an effective paradigm for the optimization of expensive-to-sample systems. Standard BO learns the performance of a system $f(x)$ by using a Gaussian Process (GP) model; this treats the system as a black-box and limits its ability to exploit available structural knowledge (e.g., physics and sparse interconnections in a complex system). Grey-box modeling, wherein the performance function is treated as a composition of known and unknown intermediate functions $f(x, y(x))$ (where $y(x)$ is a GP model) offers a solution to this limitation; however, generating an analytical probability density for $f$ from the Gaussian density of $y(x)$ is often an intractable problem (e.g., when $f$ is nonlinear). Previous work has handled this issue by using sampling techniques or by solving an auxiliary problem over an augmented space where the values of $y(x)$ are constrained by confidence intervals derived from the GP models; such solutions are computationally intensive. In this work, we provide a detailed implementation of a recently proposed grey-box BO paradigm, BOIS, that uses adaptive linearizations of $f$ to obtain analytical expressions for the statistical moments of the composite function. We show that the BOIS approach enables the exploitation of structural knowledge, such as that arising in interconnected systems as well as systems that embed multiple GP models and combinations of physics and GP models. We benchmark the effectiveness of BOIS against standard BO and existing grey-box BO algorithms using a pair of case studies focused on chemical process optimization and design. Our results indicate that BOIS performs as well as or better than existing grey-box methods, while also being less computationally intensive.
This study presents a machine learning approach to predict the number of barges transported by vessels on inland waterways using tracking data from the Automatic Identification System (AIS). While AIS tracks the location of tug and tow vessels, it does not monitor the presence or number of barges transported by those vessels. Understanding the number and types of barges conveyed along river segments, between ports, and at ports is crucial for estimating the quantities of freight transported on the nation's waterways. This insight is also valuable for waterway management and infrastructure operations impacting areas such as targeted dredging operations, and data-driven resource allocation. Labeled sample data was generated using observations from traffic cameras located along key river segments and matched to AIS data records. A sample of 164 vessels representing up to 42 barge convoys per vessel was used for model development. The methodology involved first predicting barge presence and then predicting barge quantity. Features derived from the AIS data included speed measures, vessel characteristics, turning measures, and interaction terms. For predicting barge presence, the AdaBoost model achieved an F1 score of 0.932. For predicting barge quantity, the Random Forest combined with an AdaBoost ensemble model achieved an F1 score of 0.886. Bayesian optimization was used for hyperparameter tuning. By advancing predictive modeling for inland waterways, this study offers valuable insights for transportation planners and organizations, which require detailed knowledge of traffic volumes, including the flow of commodities, their destinations, and the tonnage moving in and out of ports.
Bayesian optimization is an effective technique for black-box optimization, but its applicability is typically limited to low-dimensional and small-budget problems due to the cubic complexity of computing the Gaussian process (GP) surrogate. While various approximate GP models have been employed to scale Bayesian optimization to larger sample sizes, most suffer from overly-smooth estimation and focus primarily on problems that allow for large online samples. In this work, we argue that Bayesian optimization algorithms with sparse GPs can more efficiently allocate their representational power to relevant regions of the search space. To achieve this, we propose focalized GP, which leverages a novel variational loss function to achieve stronger local prediction, as well as FocalBO, which hierarchically optimizes the focalized GP acquisition function over progressively smaller search spaces. Experimental results demonstrate that FocalBO can efficiently leverage large amounts of offline and online data to achieve state-of-the-art performance on robot morphology design and to control a 585-dimensional musculoskeletal system.
Learning to move is a primary goal for animals and robots, where ensuring safety is often important when optimizing control policies on the embodied systems. For complex tasks such as the control of human or humanoid control, the high-dimensional parameter space adds complexity to the safe optimization effort. Current safe exploration algorithms exhibit inefficiency and may even become infeasible with large high-dimensional input spaces. Furthermore, existing high-dimensional constrained optimization methods neglect safety in the search process. In this paper, we propose High-dimensional Safe Bayesian Optimization with local optimistic exploration (HdSafeBO), a novel approach designed to handle high-dimensional sampling problems under probabilistic safety constraints. We introduce a local optimistic strategy to efficiently and safely optimize the objective function, providing a probabilistic safety guarantee and a cumulative safety violation bound. Through the use of isometric embedding, HdSafeBO addresses problems ranging from a few hundred to several thousand dimensions while maintaining safety guarantees. To our knowledge, HdSafeBO is the first algorithm capable of optimizing the control of high-dimensional musculoskeletal systems with high safety probability. We also demonstrate the real-world applicability of HdSafeBO through its use in the safe online optimization of neural stimulation induced human motion control.
Bayesian optimization (BO) with Gaussian process (GP) surrogate models is a powerful black-box optimization method. Acquisition functions are a critical part of a BO algorithm as they determine how the new samples are selected. Some of the most widely used acquisition functions include upper confidence bound (UCB) and Thompson sampling (TS). The convergence analysis of BO algorithms has focused on the cumulative regret under both the Bayesian and frequentist settings for the objective. In this paper, we establish new pointwise bounds on the prediction error of GP under the frequentist setting with Gaussian noise. Consequently, we prove improved convergence rates of cumulative regret bound for both GP-UCB and GP-TS. Of note, the new prediction error bound under Gaussian noise can be applied to general BO algorithms and convergence analysis, e.g., the asymptotic convergence of expected improvement (EI) with noise.
With the rapid development of generative artificial intelligence, particularly large language models a number of sub-fields of deep learning have made significant progress and are now very useful in everyday applications. For example,financial institutions simulate a wide range of scenarios for various models created by their research teams using reinforcement learning, both before production and after regular operations. In this work, we propose a backdoor attack that focuses solely on data poisoning and a method of detection by dynamic systems and statistical analysis of the distribution of data. This particular backdoor attack is classified as an attack without prior consideration or trigger, and we name it FinanceLLMsBackRL. Our aim is to examine the potential effects of large language models that use reinforcement learning systems for text production or speech recognition, finance, physics, or the ecosystem of contemporary artificial intelligence models.
Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics, engineering, and machine learning. This paper focuses on bilevel optimization where both upper-level and lower-level functions are black boxes and expensive to evaluate. We propose a Bayesian Optimization framework that models the upper and lower-level functions as Gaussian processes over the combined space of upper and lower-level decisions, allowing us to exploit knowledge transfer between different sub-problems. Additionally, we propose a novel acquisition function for this model. Our experimental results demonstrate that the proposed algorithm is highly sample-efficient and outperforms existing methods in finding high-quality solutions.
Spatially varying regularization accommodates the deformation variations that may be necessary for different anatomical regions during deformable image registration. Historically, optimization-based registration models have harnessed spatially varying regularization to address anatomical subtleties. However, most modern deep learning-based models tend to gravitate towards spatially invariant regularization, wherein a homogenous regularization strength is applied across the entire image, potentially disregarding localized variations. In this paper, we propose a hierarchical probabilistic model that integrates a prior distribution on the deformation regularization strength, enabling the end-to-end learning of a spatially varying deformation regularizer directly from the data. The proposed method is straightforward to implement and easily integrates with various registration network architectures. Additionally, automatic tuning of hyperparameters is achieved through Bayesian optimization, allowing efficient identification of optimal hyperparameters for any given registration task. Comprehensive evaluations on publicly available datasets demonstrate that the proposed method significantly improves registration performance and enhances the interpretability of deep learning-based registration, all while maintaining smooth deformations.
Combinatorial libraries are a powerful approach for exploring the evolution of physical properties across binary and ternary cross-sections in multicomponent phase diagrams. Although the synthesis of these libraries has been developed since the 1960s and expedited with advanced laboratory automation, the broader application of combinatorial libraries relies on fast, reliable measurements of concentration-dependent structures and functionalities. Scanning Probe Microscopies (SPM), including piezoresponse force microscopy (PFM), offer significant potential for quantitative, functionally relevant combi-library readouts. Here we demonstrate the implementation of fully automated SPM to explore the evolution of ferroelectric properties in combinatorial libraries, focusing on Sm-doped BiFeO3 and ZnxMg1-xO systems. We also present and compare Gaussian Process-based Bayesian Optimization models for fully automated exploration, emphasizing local reproducibility (effective noise) as an essential factor in optimal experiment workflows. Automated SPM, when coupled with upstream synthesis controls, plays a pivotal role in bridging materials synthesis and characterization.
Analog circuit design can be considered as an optimization problem with the targeted circuit specifications as constraints. When stringent circuit specifications are considered, it is desired to have an optimization methodology that adapts well to heavily constrained search spaces. To this end, we propose a novel Bayesian optimization algorithm with a tiered ensemble of acquisition functions and demonstrate its considerable application potential for analog circuit design automation. Our method is the first to introduce the concept of multiple dominance among acquisition functions, allowing the search for the optimal solutions to be effectively bounded \emph{within} the predicted set of feasible solutions in a constrained search space. This has resulted in a significant reduction in constraint violations by the candidate solutions, leading to better-optimized designs within tight computational budgets. The methodology is validated in gain and area optimization of a two-stage Miller compensated operational amplifier in a 65 nm technology. In comparison to robust baselines and state-of-the-art algorithms, this method reduces constraint violations by up to 38% and improves the target objective by up to 43%. The source code of our algorithm is made available at https://github.com/riarashid/TRACE.
Jailbreaking in Large Language Models (LLMs) is a major security concern as it can deceive LLMs to generate harmful text. Yet, there is still insufficient understanding of how jailbreaking works, which makes it hard to develop effective defense strategies. We aim to shed more light into this issue: we conduct a detailed large-scale analysis of seven different jailbreak methods and find that these disagreements stem from insufficient observation samples. In particular, we introduce \textit{safety boundary}, and we find that jailbreaks shift harmful activations outside that safety boundary, where LLMs are less sensitive to harmful information. We also find that the low and the middle layers are critical in such shifts, while deeper layers have less impact. Leveraging on these insights, we propose a novel defense called \textbf{Activation Boundary Defense} (ABD), which adaptively constrains the activations within the safety boundary. We further use Bayesian optimization to selectively apply the defense method to the low and the middle layers. Our experiments on several benchmarks show that ABD achieves an average DSR of over 98\% against various forms of jailbreak attacks, with less than 2\% impact on the model's general capabilities.
Bayesian Optimization (BO) is a popular approach to optimizing expensive-to-evaluate black-box functions. Despite the success of BO, its performance may decrease exponentially as the dimensionality increases. A common framework to tackle this problem is to assume that the objective function depends on a limited set of features that lie on a low-dimensional manifold embedded in the high-dimensional ambient space. The latent space can be linear or more generally nonlinear. To learn feature mapping, existing works usually use an encode-decoder framework which is either computationally expensive or susceptible to overfittting when the labeled data is limited. This paper proposes a new approach for BO in high dimensions by exploiting a new representation of the objective function. Our approach combines a random linear projection to reduce the dimensionality, with a representation learning of the nonlinear manifold. When the geometry of the latent manifold is available, a solution to exploit this geometry is proposed for representation learning. In contrast, we use a neural network. To mitigate overfitting by using the neural network, we train the feature mapping in a geometry-aware semi-supervised manner. Our approach enables efficient optimizing of BO's acquisition function in the low-dimensional space, with the advantage of projecting back to the original high-dimensional space compared to existing works in the same setting. Finally, we show empirically that our algorithm outperforms other high-dimensional BO baselines in various synthetic functions and real applications.
Hyperparameter optimization (HPO) is critical for enhancing the performance of machine learning models, yet it often involves a computationally intensive search across a large parameter space. Traditional approaches such as Grid Search and Random Search suffer from inefficiency and limited scalability, while surrogate models like Sequential Model-based Bayesian Optimization (SMBO) rely heavily on heuristic predictions that can lead to suboptimal results. This paper presents a novel perspective on HPO by formulating it as a sequential decision-making problem and leveraging Q-learning, a reinforcement learning technique, to optimize hyperparameters. The study explores the works of H.S. Jomaa et al. and Qi et al., which model HPO as a Markov Decision Process (MDP) and utilize Q-learning to iteratively refine hyperparameter settings. The approaches are evaluated for their ability to find optimal or near-optimal configurations within a limited number of trials, demonstrating the potential of reinforcement learning to outperform conventional methods. Additionally, this paper identifies research gaps in existing formulations, including the limitations of discrete search spaces and reliance on heuristic policies, and suggests avenues for future exploration. By shifting the paradigm toward policy-based optimization, this work contributes to advancing HPO methods for scalable and efficient machine learning applications.
Bayesian Optimization (BO) is a widely-used method for optimizing expensive-to-evaluate black-box functions. Traditional BO assumes that the learner has full control over all query variables without additional constraints. However, in many real-world scenarios, controlling certain query variables may incur costs. Therefore, the learner needs to balance the selection of informative subsets for targeted learning against leaving some variables to be randomly sampled to minimize costs. This problem is known as Bayesian Optimization with cost-varying variable subsets (BOCVS). While the goal of BOCVS is to identify the optimal solution with minimal cost, previous works have only guaranteed finding the optimal solution without considering the total costs incurred. Moreover, these works assume precise knowledge of the cost for each subset, which is often unrealistic. In this paper, we propose a novel algorithm for the extension of the BOCVS problem with random and unknown costs that separates the process into exploration and exploitation phases. The exploration phase will filter out low-quality variable subsets, while the exploitation phase will leverage high-quality ones. Furthermore, we theoretically demonstrate that our algorithm achieves a sub-linear rate in both quality regret and cost regret, addressing the objective of the BOCVS problem more effectively than previous analyses. Finally, we show that our proposed algorithm outperforms comparable baselines across a wide range of benchmarks.
Ads demand forecasting for Walmart's ad products plays a critical role in enabling effective resource planning, allocation, and management of ads performance. In this paper, we introduce a comprehensive demand forecasting system that tackles hierarchical time series forecasting in business settings. Though traditional hierarchical reconciliation methods ensure forecasting coherence, they often trade off accuracy for coherence especially at lower levels and fail to capture the seasonality unique to each time-series in the hierarchy. Thus, we propose a novel framework "Multi-Stage Hierarchical Forecasting Reconciliation and Adjustment (Multi-Stage HiFoReAd)" to address the challenges of preserving seasonality, ensuring coherence, and improving accuracy. Our system first utilizes diverse models, ensembled through Bayesian Optimization (BO), achieving base forecasts. The generated base forecasts are then passed into the Multi-Stage HiFoReAd framework. The initial stage refines the hierarchy using Top-Down forecasts and "harmonic alignment." The second stage aligns the higher levels' forecasts using MinTrace algorithm, following which the last two levels undergo "harmonic alignment" and "stratified scaling", to eventually achieve accurate and coherent forecasts across the whole hierarchy. Our experiments on Walmart's internal Ads-demand dataset and 3 other public datasets, each with 4 hierarchical levels, demonstrate that the average Absolute Percentage Error from the cross-validation sets improve from 3% to 40% across levels against BO-ensemble of models (LGBM, MSTL+ETS, Prophet) as well as from 1.2% to 92.9% against State-Of-The-Art models. In addition, the forecasts at all hierarchical levels are proved to be coherent. The proposed framework has been deployed and leveraged by Walmart's ads, sales and operations teams to track future demands, make informed decisions and plan resources.
We develop the framework of Indirect Query Bayesian Optimization (IQBO), a new class of Bayesian optimization problems where the integrated feedback is given via a conditional expectation of the unknown function $f$ to be optimized. The underlying conditional distribution can be unknown and learned from data. The goal is to find the global optimum of $f$ by adaptively querying and observing in the space transformed by the conditional distribution. This is motivated by real-world applications where one cannot access direct feedback due to privacy, hardware or computational constraints. We propose the Conditional Max-Value Entropy Search (CMES) acquisition function to address this novel setting, and propose a hierarchical search algorithm to address the multi-resolution setting and improve the computational efficiency. We show regret bounds for our proposed methods and demonstrate the effectiveness of our approaches on simulated optimization tasks.
The ability to autonomously explore and resolve tasks with minimal human guidance is crucial for the self-development of embodied intelligence. Although reinforcement learning methods can largely ease human effort, it's challenging to design reward functions for real-world tasks, especially for high-dimensional robotic control, due to complex relationships among joints and tasks. Recent advancements large language models (LLMs) enable automatic reward function design. However, approaches evaluate reward functions by re-training policies from scratch placing an undue burden on the reward function, expecting it to be effective throughout the whole policy improvement process. We argue for a more practical strategy in robotic autonomy, focusing on refining existing policies with policy-dependent reward functions rather than a universal one. To this end, we propose a novel reward-policy co-evolution framework where the reward function and the learned policy benefit from each other's progressive on-the-fly improvements, resulting in more efficient and higher-performing skill acquisition. Specifically, the reward evolution process translates the robot's previous best reward function, descriptions of tasks and environment into text inputs. These inputs are used to query LLMs to generate a dynamic amount of reward function candidates, ensuring continuous improvement at each round of evolution. For policy evolution, our method generates new policy populations by hybridizing historically optimal and random policies. Through an improved Bayesian optimization, our approach efficiently and robustly identifies the most capable and plastic reward-policy combination, which then proceeds to the next round of co-evolution. Despite using less data, our approach demonstrates an average normalized improvement of 95.3% across various high-dimensional robotic skill learning tasks.
When it comes to expensive black-box optimization problems, Bayesian Optimization (BO) is a well-known and powerful solution. Many real-world applications involve a large number of dimensions, hence scaling BO to high dimension is of much interest. However, state-of-the-art high-dimensional BO methods still suffer from the curse of dimensionality, highlighting the need for further improvements. In this work, we introduce BOIDS, a novel high-dimensional BO algorithm that guides optimization by a sequence of one-dimensional direction lines using a novel tailored line-based optimization procedure. To improve the efficiency, we also propose an adaptive selection technique to identify most optimal lines for each round of line-based optimization. Additionally, we incorporate a subspace embedding technique for better scaling to high-dimensional spaces. We further provide theoretical analysis of our proposed method to analyze its convergence property. Our extensive experimental results show that BOIDS outperforms state-of-the-art baselines on various synthetic and real-world benchmark problems.
In fishery science, harvest management of size-structured stochastic populations is a long-standing and difficult problem. Rectilinear precautionary policies based on biomass and harvesting reference points have now become a standard approach to this problem. While these standard feedback policies are adapted from analytical or dynamic programming solutions assuming relatively simple ecological dynamics, they are often applied to more complicated ecological settings in the real world. In this paper we explore the problem of designing harvest control rules for partially observed, age-structured, spasmodic fish populations using tools from reinforcement learning (RL) and Bayesian optimization. Our focus is on the case of Walleye fisheries in Alberta, Canada, whose highly variable recruitment dynamics have perplexed managers and ecologists. We optimized and evaluated policies using several complementary performance metrics. The main questions we addressed were: 1. How do standard policies based on reference points perform relative to numerically optimized policies? 2. Can an observation of mean fish weight, in addition to stock biomass, aid policy decisions?
The proliferation of heterogeneous configurations in distributed systems presents significant challenges in ensuring stability and efficiency. Misconfigurations, driven by complex parameter interdependencies, can lead to critical failures. Group Testing (GT) has been leveraged to expedite troubleshooting by reducing the number of tests, as demonstrated by methods like ZebraConf. However, ZebraConf's binary-splitting strategy suffers from sequential testing, limited handling of parameter interdependencies, and susceptibility to errors such as noise and dilution. We propose Ba-ZebraConf, a novel three-dimensional Bayesian framework that addresses these limitations. It integrates (1) Bayesian Group Testing (BGT), which employs probabilistic lattice models and the Bayesian Halving Algorithm (BHA) to dynamically refine testing strategies, prioritizing high-informative parameters and adapting to real-time outcomes. Bayesian optimization tunes hyperparameters, such as pool sizes and test thresholds, to maximize testing efficiency. (2) Bayesian Optimization (BO) to automate hyperparameter tuning for test efficiency, and (3) Bayesian Risk Refinement (BRR) to iteratively capture parameter interdependencies and improve classification accuracy. Ba-ZebraConf adapts to noisy environments, captures parameter interdependencies, and scales effectively for large configuration spaces. Experimental results show that Ba-ZebraConf reduces test counts and execution time by 67% compared to ZebraConf while achieving 0% false positives and false negatives. These results establish Ba-ZebraConf as a robust and scalable solution for troubleshooting heterogeneous distributed systems.