In general, electric motor design procedures for automotive applications go through expensive trial-and-error processes or use simplified models that linearly stretch the efficiency map. In this paper, we explore the possibility of efficiently optimizing the motor design directly, using high-fidelity simulation software and derivative-free optimization solvers. In particular, we proportionally scale an already existing electric motor design in axial and radial direction, as well as the sizes of the magnets and slots separately, in commercial motor design software. We encapsulate this motor model in a vehicle model together with the transmission, simulate a candidate design on a drive cycle, and find an optimum through a Bayesian optimization solver. We showcase our framework on a small city car, and observe an energy consumption reduction of 0.13% with respect to a completely proportional scaling method, with a motor that is equipped with relatively shorter but wider magnets and slots. In the extended version of this paper, we include a comparison with the linear models, and add experiments on different drive cycles and vehicle types.
In the context of digital twins, structural health monitoring (SHM) constitutes the backbone of condition-based maintenance, facilitating the interconnection between virtual and physical assets. Guided wave propagation (GWP) is commonly employed for the inspection of structures in SHM. However, GWP is sensitive to variations in the material properties of the structure, leading to false alarms. In this direction, uncertainty quantification (UQ) is regularly applied to improve the reliability of predictions. Computational mechanics is a useful tool for the simulation of GWP, and is often applied for UQ. Even so, the application of UQ methods requires numerous simulations, while large-scale, transient numerical GWP solutions increase the computational cost. Reduced order models (ROMs) are commonly employed to provide numerical results in a limited amount of time. In this paper, we propose a machine learning (ML)-based ROM, mentioned as BO-ML-ROM, to decrease the computational time related to the simulation of the GWP. The ROM is integrated with a Bayesian optimization (BO) framework, to adaptively sample the parameters for the ROM training. The finite element method is used for the simulation of the high-fidelity models. The formulated ROM is used for forward UQ of the GWP in an aluminum plate with varying material properties. To determine the influence of each parameter perturbation, a global, variance-based sensitivity analysis is implemented based on Sobol' indices. It is shown that Bayesian optimization outperforms one-shot sampling methods, both in terms of accuracy and speed-up. The predicted results reveal the efficiency of BO-ML-ROM for GWP and demonstrate its value for UQ.
The rapid advancement of deep neural networks has significantly improved various tasks, such as image and speech recognition. However, as the complexity of these models increases, so does the computational cost and the number of parameters, making it difficult to deploy them on resource-constrained devices. This paper proposes a novel memorization-based inference (MBI) that is compute free and only requires lookups. Specifically, our work capitalizes on the inference mechanism of the recurrent attention model (RAM), where only a small window of input domain (glimpse) is processed in a one time step, and the outputs from multiple glimpses are combined through a hidden vector to determine the overall classification output of the problem. By leveraging the low-dimensionality of glimpse, our inference procedure stores key value pairs comprising of glimpse location, patch vector, etc. in a table. The computations are obviated during inference by utilizing the table to read out key-value pairs and performing compute-free inference by memorization. By exploiting Bayesian optimization and clustering, the necessary lookups are reduced, and accuracy is improved. We also present in-memory computing circuits to quickly look up the matching key vector to an input query. Compared to competitive compute-in-memory (CIM) approaches, MBI improves energy efficiency by almost 2.7 times than multilayer perceptions (MLP)-CIM and by almost 83 times than ResNet20-CIM for MNIST character recognition.
When applied to open-domain question answering, large language models (LLMs) frequently generate incorrect responses based on made-up facts, which are called $\textit{hallucinations}$. Retrieval augmented generation (RAG) is a promising strategy to avoid hallucinations, but it does not provide guarantees on its correctness. To address this challenge, we propose the Trustworthy Retrieval Augmented Question Answering, or $\textit{TRAQ}$, which provides the first end-to-end statistical correctness guarantee for RAG. TRAQ uses conformal prediction, a statistical technique for constructing prediction sets that are guaranteed to contain the semantically correct response with high probability. Additionally, TRAQ leverages Bayesian optimization to minimize the size of the constructed sets. In an extensive experimental evaluation, we demonstrate that TRAQ provides the desired correctness guarantee while reducing prediction set size by 16.2% on average compared to an ablation. The implementation is available at $\href{https://github.com/shuoli90/TRAQ.git}{TRAQ}$.
Bayesian optimization (BO) is a popular method to optimize costly black-box functions. While traditional BO optimizes each new target task from scratch, meta-learning has emerged as a way to leverage knowledge from related tasks to optimize new tasks faster. However, existing meta-learning BO methods rely on surrogate models that suffer from scalability issues and are sensitive to observations with different scales and noise types across tasks. Moreover, they often overlook the uncertainty associated with task similarity. This leads to unreliable task adaptation when only limited observations are obtained or when the new tasks differ significantly from the related tasks. To address these limitations, we propose a novel meta-learning BO approach that bypasses the surrogate model and directly learns the utility of queries across tasks. Our method explicitly models task uncertainty and includes an auxiliary model to enable robust adaptation to new tasks. Extensive experiments show that our method demonstrates strong anytime performance and outperforms state-of-the-art meta-learning BO methods in various benchmarks.
Scalarization is a general, parallizable technique that can be deployed in any multiobjective setting to reduce multiple objectives into one, yet some have dismissed this versatile approach because linear scalarizations cannot explore concave regions of the Pareto frontier. To that end, we aim to find simple non-linear scalarizations that provably explore a diverse set of $k$ objectives on the Pareto frontier, as measured by the dominated hypervolume. We show that hypervolume scalarizations with uniformly random weights achieves an optimal sublinear hypervolume regret bound of $O(T^{-1/k})$, with matching lower bounds that preclude any algorithm from doing better asymptotically. For the setting of multiobjective stochastic linear bandits, we utilize properties of hypervolume scalarizations to derive a novel non-Euclidean analysis to get regret bounds of $\tilde{O}( d T^{-1/2} + T^{-1/k})$, removing unnecessary $\text{poly}(k)$ dependencies. We support our theory with strong empirical performance of using non-linear scalarizations that outperforms both their linear counterparts and other standard multiobjective algorithms in a variety of natural settings.
Impactful applications such as materials discovery, hardware design, neural architecture search, or portfolio optimization require optimizing high-dimensional black-box functions with mixed and combinatorial input spaces. While Bayesian optimization has recently made significant progress in solving such problems, an in-depth analysis reveals that the current state-of-the-art methods are not reliable. Their performances degrade substantially when the unknown optima of the function do not have a certain structure. To fill the need for a reliable algorithm for combinatorial and mixed spaces, this paper proposes Bounce that relies on a novel map of various variable types into nested embeddings of increasing dimensionality. Comprehensive experiments show that Bounce reliably achieves and often even improves upon state-of-the-art performance on a variety of high-dimensional problems.
Black-box zero-th order optimization is a central primitive for applications in fields as diverse as finance, physics, and engineering. In a common formulation of this problem, a designer sequentially attempts candidate solutions, receiving noisy feedback on the value of each attempt from the system. In this paper, we study scenarios in which feedback is also provided on the safety of the attempted solution, and the optimizer is constrained to limit the number of unsafe solutions that are tried throughout the optimization process. Focusing on methods based on Bayesian optimization (BO), prior art has introduced an optimization scheme -- referred to as SAFEOPT -- that is guaranteed not to select any unsafe solution with a controllable probability over feedback noise as long as strict assumptions on the safety constraint function are met. In this paper, a novel BO-based approach is introduced that satisfies safety requirements irrespective of properties of the constraint function. This strong theoretical guarantee is obtained at the cost of allowing for an arbitrary, controllable but non-zero, rate of violation of the safety constraint. The proposed method, referred to as SAFE-BOCP, builds on online conformal prediction (CP) and is specialized to the cases in which feedback on the safety constraint is either noiseless or noisy. Experimental results on synthetic and real-world data validate the advantages and flexibility of the proposed SAFE-BOCP.
Optimal design is a critical yet challenging task within many applications. This challenge arises from the need for extensive trial and error, often done through simulations or running field experiments. Fortunately, sequential optimal design, also referred to as Bayesian optimization when using surrogates with a Bayesian flavor, has played a key role in accelerating the design process through efficient sequential sampling strategies. However, a key opportunity exists nowadays. The increased connectivity of edge devices sets forth a new collaborative paradigm for Bayesian optimization. A paradigm whereby different clients collaboratively borrow strength from each other by effectively distributing their experimentation efforts to improve and fast-track their optimal design process. To this end, we bring the notion of consensus to Bayesian optimization, where clients agree (i.e., reach a consensus) on their next-to-sample designs. Our approach provides a generic and flexible framework that can incorporate different collaboration mechanisms. In lieu of this, we propose transitional collaborative mechanisms where clients initially rely more on each other to maneuver through the early stages with scant data, then, at the late stages, focus on their own objectives to get client-specific solutions. Theoretically, we show the sub-linear growth in regret for our proposed framework. Empirically, through simulated datasets and a real-world collaborative sensor design experiment, we show that our framework can effectively accelerate and improve the optimal design process and benefit all participants.
Controller tuning and parameter optimization are crucial in system design to improve both the controller and underlying system performance. Bayesian optimization has been established as an efficient model-free method for controller tuning and adaptation. Standard methods, however, are not enough for high-precision systems to be robust with respect to unknown input-dependent noise and stable under safety constraints. In this work, we present a novel data-driven approach, RaGoOSE, for safe controller tuning in the presence of heteroscedastic noise, combining safe learning with risk-averse Bayesian optimization. We demonstrate the method for synthetic benchmark and compare its performance to established BO-based tuning methods. We further evaluate RaGoOSE performance on a real precision-motion system utilized in semiconductor industry applications and compare it to the built-in auto-tuning routine.
In the last decades, the capacity to generate large amounts of data in science and engineering applications has been growing steadily. Meanwhile, machine learning has progressed to become a suitable tool to process and utilise the available data. Nonetheless, many relevant scientific and engineering problems present challenges where current machine learning methods cannot yet efficiently leverage the available data and resources. For example, in scientific discovery, we are often faced with the problem of exploring very large, structured and high-dimensional spaces. Moreover, the high fidelity, black-box objective function is often very expensive to evaluate. Progress in machine learning methods that can efficiently tackle such challenges would help accelerate currently crucial areas such as drug and materials discovery. In this paper, we propose a multi-fidelity active learning algorithm with GFlowNets as a sampler, to efficiently discover diverse, high-scoring candidates where multiple approximations of the black-box function are available at lower fidelity and cost. Our evaluation on molecular discovery tasks shows that multi-fidelity active learning with GFlowNets can discover high-scoring candidates at a fraction of the budget of its single-fidelity counterpart while maintaining diversity, unlike RL-based alternatives. These results open new avenues for multi-fidelity active learning to accelerate scientific discovery and engineering design.
First Order Bayesian Optimization (FOBO) is a sample efficient sequential approach to find the global maxima of an expensive-to-evaluate black-box objective function by suitably querying for the function and its gradient evaluations. Such methods assume Gaussian process (GP) models for both, the function and its gradient, and use them to construct an acquisition function that identifies the next query point. In this paper, we propose a class of practical FOBO algorithms that efficiently utilizes the information from the gradient GP to identify potential query points with zero gradients. We construct a multi-level acquisition function where in the first step, we optimize a lower level acquisition function with multiple restarts to identify potential query points with zero gradient value. We then use the upper level acquisition function to rank these query points based on their function values to potentially identify the global maxima. As a final step, the potential point of maxima is chosen as the actual query point. We validate the performance of our proposed algorithms on several test functions and show that our algorithms outperform state-of-the-art FOBO algorithms. We also illustrate the application of our algorithms in finding optimal set of hyper-parameters in machine learning and in learning the optimal policy in reinforcement learning tasks.
Learning the kernel parameters for Gaussian processes is often the computational bottleneck in applications such as online learning, Bayesian optimization, or active learning. Amortizing parameter inference over different datasets is a promising approach to dramatically speed up training time. However, existing methods restrict the amortized inference procedure to a fixed kernel structure. The amortization network must be redesigned manually and trained again in case a different kernel is employed, which leads to a large overhead in design time and training time. We propose amortizing kernel parameter inference over a complete kernel-structure-family rather than a fixed kernel structure. We do that via defining an amortization network over pairs of datasets and kernel structures. This enables fast kernel inference for each element in the kernel family without retraining the amortization network. As a by-product, our amortization network is able to do fast ensembling over kernel structures. In our experiments, we show drastically reduced inference time combined with competitive test performance for a large set of kernels and datasets.
Hyperparameter tuning of deep learning models can lead to order-of-magnitude performance gains for the same amount of compute. Despite this, systematic tuning is uncommon, particularly for large models, which are expensive to evaluate and tend to have many hyperparameters, necessitating difficult judgment calls about tradeoffs, budgets, and search bounds. To address these issues and propose a practical method for robustly tuning large models, we present Cost-Aware Pareto Region Bayesian Search (CARBS), a Bayesian optimization algorithm that performs local search around the performance-cost Pareto frontier. CARBS does well even in unbounded search spaces with many hyperparameters, learns scaling relationships so that it can tune models even as they are scaled up, and automates much of the "black magic" of tuning. Among our results, we effectively solve the entire ProcGen benchmark just by tuning a simple baseline (PPO, as provided in the original ProcGen paper). We also reproduce the model size vs. training tokens scaling result from the Chinchilla project (Hoffmann et al. 2022), while simultaneously discovering scaling laws for every other hyperparameter, via an easy automated process that uses significantly less compute and is applicable to any deep learning problem (not just language models).
Gaussian process (GP) based Bayesian optimization (BO) is a powerful method for optimizing black-box functions efficiently. The practical performance and theoretical guarantees of this approach depend on having the correct GP hyperparameter values, which are usually unknown in advance and need to be estimated from the observed data. However, in practice, these estimations could be incorrect due to biased data sampling strategies used in BO. This can lead to degraded performance and break the sub-linear global convergence guarantee of BO. To address this issue, we propose a new BO method that can sub-linearly converge to the objective function's global optimum even when the true GP hyperparameters are unknown in advance and need to be estimated from the observed data. Our method uses a multi-armed bandit technique (EXP3) to add random data points to the BO process, and employs a novel training loss function for the GP hyperparameter estimation process that ensures consistent estimation. We further provide theoretical analysis of our proposed method. Finally, we demonstrate empirically that our method outperforms existing approaches on various synthetic and real-world problems.
We propose functional causal Bayesian optimization (fCBO), a method for finding interventions that optimize a target variable in a known causal graph. fCBO extends the CBO family of methods to enable functional interventions, which set a variable to be a deterministic function of other variables in the graph. fCBO models the unknown objectives with Gaussian processes whose inputs are defined in a reproducing kernel Hilbert space, thus allowing to compute distances among vector-valued functions. In turn, this enables to sequentially select functions to explore by maximizing an expected improvement acquisition functional while keeping the typical computational tractability of standard BO settings. We introduce graphical criteria that establish when considering functional interventions allows attaining better target effects, and conditions under which selected interventions are also optimal for conditional target effects. We demonstrate the benefits of the method in a synthetic and in a real-world causal graph.
This paper presents a data-driven strategy to streamline the deployment of model-based controllers in legged robotic hardware platforms. Our approach leverages a model-free safe learning algorithm to automate the tuning of control gains, addressing the mismatch between the simplified model used in the control formulation and the real system. This method substantially mitigates the risk of hazardous interactions with the robot by sample-efficiently optimizing parameters within a probably safe region. Additionally, we extend the applicability of our approach to incorporate the different gait parameters as contexts, leading to a safe, sample-efficient exploration algorithm capable of tuning a motion controller for diverse gait patterns. We validate our method through simulation and hardware experiments, where we demonstrate that the algorithm obtains superior performance on tuning a model-based motion controller for multiple gaits safely.
Active learning parallelization is widely used, but typically relies on fixing the batch size throughout experimentation. This fixed approach is inefficient because of a dynamic trade-off between cost and speed -- larger batches are more costly, smaller batches lead to slower wall-clock run-times -- and the trade-off may change over the run (larger batches are often preferable earlier). To address this trade-off, we propose a novel Probabilistic Numerics framework that adaptively changes batch sizes. By framing batch selection as a quadrature task, our integration-error-aware algorithm facilitates the automatic tuning of batch sizes to meet predefined quadrature precision objectives, akin to how typical optimizers terminate based on convergence thresholds. This approach obviates the necessity for exhaustive searches across all potential batch sizes. We also extend this to scenarios with constrained active learning and constrained optimization, interpreting constraint violations as reductions in the precision requirement, to subsequently adapt batch construction. Through extensive experiments, we demonstrate that our approach significantly enhances learning efficiency and flexibility in diverse Bayesian batch active learning and Bayesian optimization applications.
As Transformer-based models have achieved impressive performance on various time series tasks, Long-Term Series Forecasting (LTSF) tasks have also received extensive attention in recent years. However, due to the inherent computational complexity and long sequences demanding of Transformer-based methods, its application on LTSF tasks still has two major issues that need to be further investigated: 1) Whether the sparse attention mechanism designed by these methods actually reduce the running time on real devices; 2) Whether these models need extra long input sequences to guarantee their performance? The answers given in this paper are negative. Therefore, to better copy with these two issues, we design a lightweight Period-Attention mechanism (Periodformer), which renovates the aggregation of long-term subseries via explicit periodicity and short-term subseries via built-in proximity. Meanwhile, a gating mechanism is embedded into Periodformer to regulate the influence of the attention module on the prediction results. Furthermore, to take full advantage of GPUs for fast hyperparameter optimization (e.g., finding the suitable input length), a Multi-GPU Asynchronous parallel algorithm based on Bayesian Optimization (MABO) is presented. MABO allocates a process to each GPU via a queue mechanism, and then creates multiple trials at a time for asynchronous parallel search, which greatly reduces the search time. Compared with the state-of-the-art methods, the prediction error of Periodformer reduced by 13% and 26% for multivariate and univariate forecasting, respectively. In addition, MABO reduces the average search time by 46% while finding better hyperparameters. As a conclusion, this paper indicates that LTSF may not need complex attention and extra long input sequences. The code has been open sourced on Github.
Minimizing response times is crucial for emergency medical services to reduce patients' waiting times and to increase their survival rates. Many models exist to optimize operational tasks such as ambulance allocation and dispatching. Including accurate demand forecasts in such models can improve operational decision-making. Against this background, we present a novel convolutional neural network (CNN) architecture that transforms time series data into heatmaps to predict ambulance demand. Applying such predictions requires incorporating external features that influence ambulance demands. We contribute to the existing literature by providing a flexible, generic CNN architecture, allowing for the inclusion of external features with varying dimensions. Additionally, we provide a feature selection and hyperparameter optimization framework utilizing Bayesian optimization. We integrate historical ambulance demand and external information such as weather, events, holidays, and time. To show the superiority of the developed CNN architecture over existing approaches, we conduct a case study for Seattle's 911 call data and include external information. We show that the developed CNN architecture outperforms existing state-of-the-art methods and industry practice by more than 9%.