Parallelisation in Bayesian optimisation is a common strategy but faces several challenges: the need for flexibility in acquisition functions and kernel choices, flexibility dealing with discrete and continuous variables simultaneously, model misspecification, and lastly fast massive parallelisation. To address these challenges, we introduce a versatile and modular framework for batch Bayesian optimisation via probabilistic lifting with kernel quadrature, called SOBER, which we present as a Python library based on GPyTorch/BoTorch. Our framework offers the following unique benefits: (1) Versatility in downstream tasks under a unified approach. (2) A gradient-free sampler, which does not require the gradient of acquisition functions, offering domain-agnostic sampling (e.g., discrete and mixed variables, non-Euclidean space). (3) Flexibility in domain prior distribution. (4) Adaptive batch size (autonomous determination of the optimal batch size). (5) Robustness against a misspecified reproducing kernel Hilbert space. (6) Natural stopping criterion.
Large Language Models (LLMs) have exhibited remarkable proficiency in comprehending and generating natural language. On the other hand, personalized LLM response generation holds the potential to offer substantial benefits for individuals in critical areas such as medical. Existing research has explored memory-augmented methods to prompt the LLM with pre-stored user-specific knowledge for personalized response generation in terms of new queries. We contend that such paradigm is unable to perceive fine-granularity information. In this study, we propose a novel \textbf{M}emory-\textbf{i}njected approach using parameter-efficient fine-tuning (PEFT) and along with a Bayesian Optimisation searching strategy to achieve \textbf{L}LM \textbf{P}ersonalization(\textbf{MiLP}).
Minimising cycle time without inducing quality defects is a major challenge in the injection moulding (IM). Design of Experiment methods (DoE) have been widely studied for optimisation of the IM, however existing methods have limitations, including the need for a large number of experiments and a pre-determined search space. Bayesian adaptive design of experiment (ADoE) is an iterative process where the results of the previous experiments are used to make an informed selection for the next design. In this study, for the first time, an experimental ADoE approach, based on Bayesian optimisation, was developed in injection moulding using process and sensor data to optimise the quality and cycle time in real-time. A novel approach for the real-time characterisation of post-production shrinkage was introduced, utilising in-mould sensor data on temperature differential during part cooling. This characterisation approach was verified by post-production metrology results. A single and multi-objective optimisation of the cycle time and temperature differential in an injection moulded component is proposed. The multi-objective optimisation techniques, composite desirability function and Nondominated Sorting Genetic Algorithm (NSGA-II) using Response Surface Methodology (RSM) model, are compared with the real-time novel ADoE approach. ADoE achieved almost a 50% reduction in the number of experiments required for the single optimisation of temperature differential, and an almost 30% decrease for the optimisation of temperature differential and cycle time together compared to composite desirability function and NSGA-II. Also, the optimal settings identified by ADoE for multiobjective optimisation were similar to the selected Pareto optimal solution found by the NSGA-II.
Experiments in engineering are typically conducted in controlled environments where parameters can be set to any desired value. This assumes that the same applies in a real-world setting -- an assumption that is often incorrect as many experiments are influenced by uncontrollable environmental conditions such as temperature, humidity and wind speed. When optimising such experiments, the focus should lie on finding optimal values conditionally on these uncontrollable variables. This article extends Bayesian optimisation to the optimisation of systems in changing environments that include controllable and uncontrollable parameters. The extension fits a global surrogate model over all controllable and environmental variables but optimises only the controllable parameters conditional on measurements of the uncontrollable variables. The method is validated on two synthetic test functions and the effects of the noise level, the number of the environmental parameters, the parameter fluctuation, the variability of the uncontrollable parameters, and the effective domain size are investigated. ENVBO, the proposed algorithm resulting from this investigation, is applied to a wind farm simulator with eight controllable and one environmental parameter. ENVBO finds solutions for the full domain of the environmental variable that outperforms results from optimisation algorithms that only focus on a fixed environmental value in all but one case while using a fraction of their evaluation budget. This makes the proposed approach very sample-efficient and cost-effective. An off-the-shelf open-source version of ENVBO is available via the NUBO Python package.
Bayesian optimisation requires fitting a Gaussian process model, which in turn requires specifying prior on the unknown black-box function -- most of the theoretical literature assumes this prior is known. However, it is common to have more than one possible prior for a given black-box function, for example suggested by domain experts with differing opinions. In some cases, the type-II maximum likelihood estimator for selecting prior enjoys the consistency guarantee, but it does not universally apply to all types of priors. If the problem is stationary, one could rely on the Regret Balancing scheme to conduct the optimisation, but in the case of time-varying problems, such a scheme cannot be used. To address this gap in existing research, we propose a novel algorithm, PE-GP-UCB, which is capable of solving time-varying Bayesian optimisation problems even without the exact knowledge of the function's prior. The algorithm relies on the fact that either the observed function values are consistent with some of the priors, in which case it is easy to reject the wrong priors, or the observations are consistent with all candidate priors, in which case it does not matter which prior our model relies on. We provide a regret bound on the proposed algorithm. Finally, we empirically evaluate our algorithm on toy and real-world time-varying problems and show that it outperforms the maximum likelihood estimator, fully Bayesian treatment of unknown prior and Regret Balancing.
Positive-Unlabelled (PU) learning is a growing field of machine learning that aims to learn classifiers from data consisting of labelled positive and unlabelled instances, which can be in reality positive or negative, but whose label is unknown. An extensive number of methods have been proposed to address PU learning over the last two decades, so many so that selecting an optimal method for a given PU learning task presents a challenge. Our previous work has addressed this by proposing GA-Auto-PU, the first Automated Machine Learning (Auto-ML) system for PU learning. In this work, we propose two new Auto-ML systems for PU learning: BO-Auto-PU, based on a Bayesian Optimisation approach, and EBO-Auto-PU, based on a novel evolutionary/Bayesian optimisation approach. We also present an extensive evaluation of the three Auto-ML systems, comparing them to each other and to well-established PU learning methods across 60 datasets (20 real-world datasets, each with 3 versions in terms of PU learning characteristics).
Machine learning has emerged as a powerful solution to the modern challenges in accelerator physics. However, the limited availability of beam time, the computational cost of simulations, and the high-dimensionality of optimisation problems pose significant challenges in generating the required data for training state-of-the-art machine learning models. In this work, we introduce Cheetah, a PyTorch-based high-speed differentiable linear-beam dynamics code. Cheetah enables the fast collection of large data sets by reducing computation times by multiple orders of magnitude and facilitates efficient gradient-based optimisation for accelerator tuning and system identification. This positions Cheetah as a user-friendly, readily extensible tool that integrates seamlessly with widely adopted machine learning tools. We showcase the utility of Cheetah through five examples, including reinforcement learning training, gradient-based beamline tuning, gradient-based system identification, physics-informed Bayesian optimisation priors, and modular neural network surrogate modelling of space charge effects. The use of such a high-speed differentiable simulation code will simplify the development of machine learning-based methods for particle accelerators and fast-track their integration into everyday operations of accelerator facilities.
Multi-fidelity Bayesian Optimisation (MFBO) has been shown to generally converge faster than single-fidelity Bayesian Optimisation (SFBO) (Poloczek et al. (2017)). Inspired by recent benchmark papers, we are investigating the long-run behaviour of MFBO, based on observations in the literature that it might under-perform in certain scenarios (Mikkola et al. (2023), Eggensperger et al. (2021)). An under-performance of MBFO in the long-run could significantly undermine its application to many research tasks, especially when we are not able to identify when the under-performance begins. We create a simple benchmark study, showcase empirical results and discuss scenarios and possible reasons of under-performance.
Design optimisation potentially leads to lightweight aircraft structures with lower environmental impact. Due to the high number of design variables and constraints, these problems are ordinarily solved using gradient-based optimisation methods, leading to a local solution in the design space while the global space is neglected. Bayesian Optimisation is a promising path towards sample-efficient, global optimisation based on probabilistic surrogate models. While Bayesian optimisation methods have demonstrated their strength for problems with a low number of design variables, the scalability to high-dimensional problems while incorporating large-scale constraints is still lacking. Especially in aeroelastic tailoring where directional stiffness properties are embodied into the structural design of aircraft, to control aeroelastic deformations and to increase the aerodynamic and structural performance, the safe operation of the system needs to be ensured by involving constraints resulting from different analysis disciplines. Hence, a global design space search becomes even more challenging. The present study attempts to tackle the problem by using high-dimensional Bayesian Optimisation in combination with a dimensionality reduction approach to solve the optimisation problem occurring in aeroelastic tailoring, presenting a novel approach for high-dimensional problems with large-scale constraints. Experiments on well-known benchmark cases with black-box constraints show that the proposed approach can incorporate large-scale constraints.
Many applications in Reinforcement Learning (RL) usually have noise or stochasticity present in the environment. Beyond their impact on learning, these uncertainties lead the exact same policy to perform differently, i.e. yield different return, from one roll-out to another. Common evaluation procedures in RL summarise the consequent return distributions using solely the expected return, which does not account for the spread of the distribution. Our work defines this spread as the policy reproducibility: the ability of a policy to obtain similar performance when rolled out many times, a crucial property in some real-world applications. We highlight that existing procedures that only use the expected return are limited on two fronts: first an infinite number of return distributions with a wide range of performance-reproducibility trade-offs can have the same expected return, limiting its effectiveness when used for comparing policies; second, the expected return metric does not leave any room for practitioners to choose the best trade-off value for considered applications. In this work, we address these limitations by recommending the use of Lower Confidence Bound, a metric taken from Bayesian optimisation that provides the user with a preference parameter to choose a desired performance-reproducibility trade-off. We also formalise and quantify policy reproducibility, and demonstrate the benefit of our metrics using extensive experiments of popular RL algorithms on common uncertain RL tasks.
We introduce GAUCHE, a library for GAUssian processes in CHEmistry. Gaussian processes have long been a cornerstone of probabilistic machine learning, affording particular advantages for uncertainty quantification and Bayesian optimisation. Extending Gaussian processes to chemical representations, however, is nontrivial, necessitating kernels defined over structured inputs such as graphs, strings and bit vectors. By defining such kernels in GAUCHE, we seek to open the door to powerful tools for uncertainty quantification and Bayesian optimisation in chemistry. Motivated by scenarios frequently encountered in experimental chemistry, we showcase applications for GAUCHE in molecular discovery and chemical reaction optimisation. The codebase is made available at https://github.com/leojklarner/gauche
Self-driving laboratories (SDLs) consist of multiple stations that perform material synthesis and characterisation tasks. To minimize station downtime and maximize experimental throughput, it is practical to run experiments in asynchronous parallel, in which multiple experiments are being performed at once in different stages. Asynchronous parallelization of experiments, however, introduces delayed feedback (i.e. "pending experiments"), which is known to reduce Bayesian optimiser performance. Here, we build a simulator for a multi-stage SDL and compare optimisation strategies for dealing with delayed feedback and asynchronous parallelized operation. Using data from a real SDL, we build a ground truth Bayesian optimisation simulator from 177 previously run experiments for maximizing the conductivity of functional coatings. We then compare search strategies such as expected improvement, noisy expected improvement, 4-mode exploration and random sampling. We evaluate their performance in terms of amount of delay and problem dimensionality. Our simulation results showcase the trade-off between the asynchronous parallel operation and delayed feedback.
Domain experts often possess valuable physical insights that are overlooked in fully automated decision-making processes such as Bayesian optimisation. In this article we apply high-throughput (batch) Bayesian optimisation alongside anthropological decision theory to enable domain experts to influence the selection of optimal experiments. Our methodology exploits the hypothesis that humans are better at making discrete choices than continuous ones and enables experts to influence critical early decisions. At each iteration we solve an augmented multi-objective optimisation problem across a number of alternate solutions, maximising both the sum of their utility function values and the determinant of their covariance matrix, equivalent to their total variability. By taking the solution at the knee point of the Pareto front, we return a set of alternate solutions at each iteration that have both high utility values and are reasonably distinct, from which the expert selects one for evaluation. We demonstrate that even in the case of an uninformed practitioner, our algorithm recovers the regret of standard Bayesian optimisation.
Transfer learning for Bayesian optimisation has generally assumed a strong similarity between optimisation tasks, with at least a subset having similar optimal inputs. This assumption can reduce computational costs, but it is violated in a wide range of optimisation problems where transfer learning may nonetheless be useful. We replace this assumption with a weaker one only requiring the shape of the optimisation landscape to be similar, and analyse the recent method Prior Learning for Bayesian Optimisation - PLeBO - in this setting. By learning priors for the hyperparameters of the Gaussian process surrogate model we can better approximate the underlying function, especially for few function evaluations. We validate the learned priors and compare to a breadth of transfer learning approaches, using synthetic data and a recent air pollution optimisation problem as benchmarks. We show that PLeBO and prior transfer find good inputs in fewer evaluations.
A Bayesian optimization approach for maximizing the gas conversion rate in an industrial-scale bioreactor for syngas fermentation is presented. We have access to a high-fidelity, computational fluid dynamic (CFD) reactor model and a low-fidelity ideal-mixing-based reactor model. The goal is to maximize the gas conversion rate, with respect to the input variables (e.g., pressure, biomass concentration, gas flow rate). Due to the high cost of the CFD reactor model, a multi-fidelity Bayesian optimization algorithm is adopted to solve the optimization problem using both high and low fidelities. We first describe the problem in the context of syngas fermentation followed by our approach to solving simulator optimization using multiple fidelities. We discuss concerns regarding significant differences in fidelity cost and their impact on fidelity sampling and conclude with a discussion on the integration of real-world fermentation data.
A forecasting ensemble consisting of a diverse range of estimators for both local and global univariate forecasting, in particular MQ-CNN,DeepAR, Prophet, NPTS, ARIMA and ETS, can be used to make forecasts for a variety of problems. This paper delves into the aspect of adding different hyperparameter optimization strategies to the deep learning models in such a setup (DeepAR and MQ-CNN), exploring the trade-off between added training cost and the increase in accuracy for different configurations. It shows that in such a setup, adding hyperparameter optimization can lead to performance improvements, with the final setup having a 9.9 % percent accuracy improvement with respect to the avg-wQL over the baseline ensemble without HPO, accompanied by a 65.8 % increase in end-to-end ensemble latency. This improvement is based on an empirical analysis of combining the ensemble pipeline with different tuning strategies, namely Bayesian Optimisation and Hyperband and different configurations of those strategies. In the final configuration, the proposed combination of ensemble learning and HPO outperforms the state of the art commercial AutoML forecasting solution, Amazon Forecast, with a 3.5 % lower error and 16.0 % lower end-to-end ensemble latency.
To enable closed form conditioning, a common assumption in Gaussian process (GP) regression is independent and identically distributed Gaussian observation noise. This strong and simplistic assumption is often violated in practice, which leads to unreliable inferences and uncertainty quantification. Unfortunately, existing methods for robustifying GPs break closed-form conditioning, which makes them less attractive to practitioners and significantly more computationally expensive. In this paper, we demonstrate how to perform provably robust and conjugate Gaussian process (RCGP) regression at virtually no additional cost using generalised Bayesian inference. RCGP is particularly versatile as it enables exact conjugate closed form updates in all settings where standard GPs admit them. To demonstrate its strong empirical performance, we deploy RCGP for problems ranging from Bayesian optimisation to sparse variational Gaussian processes.
As is well known, both sampling from the posterior and computing the mean of the posterior in Gaussian process regression reduces to solving a large linear system of equations. We study the use of stochastic gradient descent for solving this linear system, and show that when \emph{done right} -- by which we mean using specific insights from the optimisation and kernel communities -- stochastic gradient descent is highly effective. To that end, we introduce a particularly simple \emph{stochastic dual descent} algorithm, explain its design in an intuitive manner and illustrate the design choices through a series of ablation studies. Further experiments demonstrate that our new method is highly competitive. In particular, our evaluations on the UCI regression tasks and on Bayesian optimisation set our approach apart from preconditioned conjugate gradients and variational Gaussian process approximations. Moreover, our method places Gaussian process regression on par with state-of-the-art graph neural networks for molecular binding affinity prediction.
Nuclear fusion using magnetic confinement holds promise as a viable method for sustainable energy. However, most fusion devices have been experimental and as we move towards energy reactors, we are entering into a new paradigm of engineering. Curating a design for a fusion reactor is a high-dimensional multi-output optimisation process. Through this work we demonstrate a proof-of-concept of an AI-driven strategy to help explore the design search space and identify optimum parameters. By utilising a Multi-Output Bayesian Optimisation scheme, our strategy is capable of identifying the Pareto front associated with the optimisation of the toroidal field coil shape of a tokamak. The optimisation helps to identify design parameters that would minimise the costs incurred while maximising the plasma stability by way of minimising magnetic ripples.
Reinforcement learning is well known for its ability to model sequential tasks and learn latent data patterns adaptively. Deep learning models have been widely explored and adopted in regression and classification tasks. However, deep learning has its limitations such as the assumption of equally spaced and ordered data, and the lack of ability to incorporate graph structure in terms of time-series prediction. Graphical neural network (GNN) has the ability to overcome these challenges and capture the temporal dependencies in time-series data. In this study, we propose a novel approach for predicting time-series data using GNN and monitoring with Reinforcement Learning (RL). GNNs are able to explicitly incorporate the graph structure of the data into the model, allowing them to capture temporal dependencies in a more natural way. This approach allows for more accurate predictions in complex temporal structures, such as those found in healthcare, traffic and weather forecasting. We also fine-tune our GraphRL model using a Bayesian optimisation technique to further improve performance. The proposed framework outperforms the baseline models in time-series forecasting and monitoring. The contributions of this study include the introduction of a novel GraphRL framework for time-series prediction and the demonstration of the effectiveness of GNNs in comparison to traditional deep learning models such as RNNs and LSTMs. Overall, this study demonstrates the potential of GraphRL in providing accurate and efficient predictions in dynamic RL environments.