The signature kernel is a kernel between time series of arbitrary length and comes with strong theoretical guarantees from stochastic analysis. It has found applications in machine learning such as covariance functions for Gaussian processes. A strength of the underlying signature features is that they provide a structured global description of a time series. However, this property can quickly become a curse when local information is essential and forgetting is required; so far this has only been addressed with ad-hoc methods such as slicing the time series into smaller segments. To overcome this, we propose a principled and data-driven approach by introducing a novel forgetting mechanism for signature features. This allows the model to dynamically adapt its observed context length to focus on more recent information. To achieve this, we revisit the recently introduced Random Fourier Signature Features, and develop Random Fourier Decayed Signature Features (RFDSF) with Gaussian processes (GPs). This results in a Bayesian time series forecasting algorithm with variational inference, that offers a scalable probabilistic algorithm that processes and transforms a time series into a joint predictive distribution over the time steps in one pass using recurrence. For example, processing a sequence of length $10^4$ steps in less than $10^{-2}$ seconds and in $\approx$ 1GB of GPU memory. We demonstrate that the algorithm outperforms other GP-based alternatives and competes with state-of-the-art probabilistic time series forecasting algorithms.

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.

Despite the importance of aligning language models with human preferences, crowd-sourced human feedback is often noisy---for example, preferring less desirable responses---posing a fundamental challenge to alignment. A truly robust alignment objective should yield identical model parameters even under severe label noise, a property known as redescending. We prove that no existing alignment methods satisfy this property. To address this, we propose Hölder-DPO, the first principled alignment loss with a provable redescending property, enabling estimation of the clean data distribution from noisy feedback. The aligned model estimates the likelihood of clean data, providing a theoretically grounded metric for dataset valuation that identifies the location and fraction of mislabels. This metric is gradient-free, enabling scalable and automated human feedback valuation without costly manual verification or clean validation dataset. Hölder-DPO achieves state-of-the-art robust alignment performance while accurately detecting mislabels in controlled datasets. Finally, applied to Anthropic HH-RLHF dataset, it reveals substantial noise levels and removing these mislabels significantly improves alignment performance across methods. The code is available at https://github.com/ma921/HolderDPO.

In spite of their prevalence, the behaviour of Neural Networks when extrapolating far from the training distribution remains poorly understood, with existing results limited to specific cases. In this work, we prove general results---the first of their kind---by applying Neural Tangent Kernel (NTK) theory to analyse infinitely-wide neural networks trained until convergence and prove that the inclusion of just one Layer Norm (LN) fundamentally alters the induced NTK, transforming it into a bounded-variance kernel. As a result, the output of an infinitely wide network with at least one LN remains bounded, even on inputs far from the training data. In contrast, we show that a broad class of networks without LN can produce pathologically large outputs for certain inputs. We support these theoretical findings with empirical experiments on finite-width networks, demonstrating that while standard NNs often exhibit uncontrolled growth outside the training domain, a single LN layer effectively mitigates this instability. Finally, we explore real-world implications of this extrapolatory stability, including applications to predicting residue sizes in proteins larger than those seen during training and estimating age from facial images of underrepresented ethnicities absent from the training set.

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.

Like many optimizers, Bayesian optimization often falls short of gaining user trust due to opacity. While attempts have been made to develop human-centric optimizers, they typically assume user knowledge is well-specified and error-free, employing users mainly as supervisors of the optimization process. We relax these assumptions and propose a more balanced human-AI partnership with our Collaborative and Explainable Bayesian Optimization (CoExBO) framework. Instead of explicitly requiring a user to provide a knowledge model, CoExBO employs preference learning to seamlessly integrate human insights into the optimization, resulting in algorithmic suggestions that resonate with user preference. CoExBO explains its candidate selection every iteration to foster trust, empowering users with a clearer grasp of the optimization. Furthermore, CoExBO offers a no-harm guarantee, allowing users to make mistakes; even with extreme adversarial interventions, the algorithm converges asymptotically to a vanilla Bayesian optimization. We validate CoExBO’s efficacy through human-AI teaming experiments in lithium-ion battery design, highlighting substantial improvements over conventional methods. Code is available https://github.com/ma921/CoExBO.

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.

Bayesian optimisation for real-world problems is often performed interactively with human experts, and integrating their domain knowledge is key to accelerate the optimisation process. We consider a setup where experts provide advice on the next query point through binary accept/reject recommendations (labels). Experts’ labels are often costly, requiring efficient use of their efforts, and can at the same time be unreliable, requiring careful adjustment of the degree to which any expert is trusted. We introduce the first principled approach that provides two key guarantees. (1) Handover guarantee: similar to a no-regret property, we establish a sublinear bound on the cumulative number of experts’ binary labels. Initially, multiple labels per query are needed, but the number of expert labels required asymptotically converges to zero, saving both expert effort and computation time. (2) No-harm guarantee with data-driven trust level adjustment: our adaptive trust level ensures that the convergence rate will not be worse than the one without using advice, even if the advice from experts is adversarial. Unlike existing methods that employ a user-defined function that hand-tunes the trust level adjustment, our approach enables data-driven adjustments. Real-world applications empirically demonstrate that our method not only outperforms existing baselines, but also maintains robustness despite varying labelling accuracy, in tasks of battery design with human experts.

Bayesian Optimization (BO) is widely used for optimising black-box functions but requires us to specify the length scale hyperparameter, which defines the smoothness of the functions the optimizer will consider. Most current BO algorithms choose this hyperparameter by maximizing the marginal likelihood of the observed data, albeit risking misspecification if the objective function is less smooth in regions we have not yet explored. The only prior solution addressing this problem with theoretical guarantees was A-GP-UCB, proposed by Berkenkamp et al. (2019). This algorithm progressively decreases the length scale, expanding the class of functions considered by the optimizer. However, A-GP-UCB lacks a stopping mechanism, leading to over-exploration and slow convergence. To overcome this, we introduce Length scale Balancing (LB) - a novel approach, aggregating multiple base surrogate models with varying length scales. LB intermittently adds smaller length scale candidate values while retaining longer scales, balancing exploration and exploitation. We formally derive a cumulative regret bound of LB and compare it with the regret of an oracle BO algorithm using the optimal length scale. Denoting the factor by which the regret bound of A-GP-UCB was away from oracle as $g(T)$, we show that LB is only $\log g(T)$ away from oracle regret. We also empirically evaluate our algorithm on synthetic and real-world benchmarks and show it outperforms A-GP-UCB and maximum likelihood estimation.

The goal of Bayesian inverse reinforcement learning (IRL) is recovering a posterior distribution over reward functions using a set of demonstrations from an expert optimizing for a reward unknown to the learner. The resulting posterior over rewards can then be used to synthesize an apprentice policy that performs well on the same or a similar task. A key challenge in Bayesian IRL is bridging the computational gap between the hypothesis space of possible rewards and the likelihood, often defined in terms of Q values: vanilla Bayesian IRL needs to solve the costly forward planning problem – going from rewards to the Q values – at every step of the algorithm, which may need to be done thousands of times. We propose to solve this by a simple change: instead of focusing on primarily sampling in the space of rewards, we can focus on primarily working in the space of Q-values, since the computation required to go from Q-values to reward is radically cheaper. Furthermore, this reversion of the computation makes it easy to compute the gradient allowing efficient sampling using Hamiltonian Monte Carlo. We propose ValueWalk – a new Markov chain Monte Carlo method based on this insight – and illustrate its advantages on several tasks.

The increasing availability of graph-structured data motivates the task of optimising over functions defined on the node set of graphs. Traditional graph search algorithms can be applied in this case, but they may be sample-inefficient and do not make use of information about the function values; on the other hand, Bayesian optimisation is a class of promising black-box solvers with superior sample efficiency, but it has scarcely been applied to such novel setups. To fill this gap, we propose a novel Bayesian optimisation framework that optimises over functions defined on generic, large-scale and potentially unknown graphs. Through the learning of suitable kernels on graphs, our framework has the advantage of adapting to the behaviour of the target function. The local modelling approach further guarantees the efficiency of our method. Extensive experiments on both synthetic and real-world graphs demonstrate the effectiveness of the proposed optimisation framework.

Marginalising over families of Gaussian Process kernels produces flexible model classes with well-calibrated uncertainty estimates. Existing approaches require likelihood evaluations of many kernels, rendering them prohibitively expensive for larger datasets. We propose a Bayesian Quadrature scheme to make this marginalisation more efficient and thereby more practical. Through use of maximum mean discrepancies between distributions, we define a kernel over kernels that captures invariances between Spectral Mixture (SM) Kernels. Kernel samples are selected by generalising an information-theoretic acquisition function for warped Bayesian Quadrature. We show that our framework achieves more accurate predictions with better calibrated uncertainty than state-of-the-art baselines, especially when given limited (wall-clock) time budgets.

Bayesian optimization (BO) is a sample-efficient approach for tuning design parameters to optimize expensive-to-evaluate, black-box performance metrics. In many manufacturing processes, the design parameters are subject to random input noise, resulting in a product that is often less performant than expected. Although BO methods have been proposed for optimizing a single objective under input noise, no existing method addresses the practical scenario where there are multiple objectives that are sensitive to input perturbations. In this work, we propose the first multi-objective BO method that is robust to input noise. We formalize our goal as optimizing the multivariate value-at-risk (MVaR), a risk measure of the uncertain objectives. Since directly optimizing MVaR is computationally infeasible in many settings, we propose a scalable, theoretically-grounded approach for optimizing MVaR using random scalarizations. Empirically, we find that our approach significantly outperforms alternative methods and efficiently identifies optimal robust designs that will satisfy specifications across multiple metrics with high probability.

Calculation of Bayesian posteriors and model evidences typically requires numerical integration. Bayesian quadrature (BQ), a surrogate-model-based approach to numerical integration, is capable of superb sample efficiency, but its lack of parallelisation has hindered its practical applications. In this work, we propose a parallelised (batch) BQ method, employing techniques from kernel quadrature, that possesses an empirically exponential convergence rate.Additionally, just as with Nested Sampling, our method permits simultaneous inference of both posteriors and model evidence.Samples from our BQ surrogate model are re-selected to give a sparse set of samples, via a kernel recombination algorithm, requiring negligible additional time to increase the batch size.Empirically, we find that our approach significantly outperforms the sampling efficiency of both state-of-the-art BQ techniques and Nested Sampling in various real-world datasets, including lithium-ion battery analytics.

Gaussian processes (GPs) produce good probabilistic models of functions, but most GP kernels require $O((n+m)n^2)$ time, where $n$ is the number of data points and $m$ the number of predictive locations. We present a new kernel that allows for Gaussian process regression in $O((n+m)\log(n+m))$ time. Our "binary tree" kernel places all data points on the leaves of a binary tree, with the kernel depending only on the depth of the deepest common ancestor. We can store the resulting kernel matrix in $O(n)$ space in $O(n \log n)$ time, as a sum of sparse rank-one matrices, and approximately invert the kernel matrix in $O(n)$ time. Sparse GP methods also offer linear run time, but they predict less well than higher dimensional kernels. On a classic suite of regression tasks, we compare our kernel against Mat\'ern, sparse, and sparse variational kernels. The binary tree GP assigns the highest likelihood to the test data on a plurality of datasets, usually achieves lower mean squared error than the sparse methods, and often ties or beats the Mat\'ern GP. On large datasets, the binary tree GP is fastest, and much faster than a Mat\'ern GP.

Optimizing expensive-to-evaluate black-box functions of discrete (and potentially continuous) design parameters is a ubiquitous problem in scientific and engineering applications. Bayesian optimization (BO) is a popular, sample-efficient method that leverages a probabilistic surrogate model and an acquisition function (AF) to select promising designs to evaluate. However, maximizing the AF over mixed or high-cardinality discrete search spaces is challenging standard gradient-based methods cannot be used directly or evaluating the AF at every point in the search space would be computationally prohibitive. To address this issue, we propose using probabilistic reparameterization (PR). Instead of directly optimizing the AF over the search space containing discrete parameters, we instead maximize the expectation of the AF over a probability distribution defined by continuous parameters. We prove that under suitable reparameterizations, the BO policy that maximizes the probabilistic objective is the same as that which maximizes the AF, and therefore, PR enjoys the same regret bounds as the original BO policy using the underlying AF. Moreover, our approach provably converges to a stationary point of the probabilistic objective under gradient ascent using scalable, unbiased estimators of both the probabilistic objective and its gradient. Therefore, as the number of starting points and gradient steps increase, our approach will recover of a maximizer of the AF (an often-neglected requisite for commonly used BO regret bounds). We validate our approach empirically and demonstrate state-of-the-art optimization performance on a wide range of real-world applications. PR is complementary to (and benefits) recent work and naturally generalizes to settings with multiple objectives and black-box constraints.

Modern approximations to Gaussian processes are suitable for tall data'', with a cost that scales well in the number of observations, but under-performs onwide data'', scaling poorly in the number of input features. That is, as the number of input features grows, good predictive performance requires the number of summarising variables, and their associated cost, to grow rapidly. We introduce a kernel that allows the number of summarising variables to grow exponentially with the number of input features, but requires only linear cost in both number of observations and input features. This scaling is achieved through our introduction of the ``Bezier buttress'', which allows approximate inference without computing matrix inverses or determinants. We show that our kernel has close similarities to some of the most used kernels in Gaussian process regression, and empirically demonstrate the kernel's ability to scale to both tall and wide datasets.

Modelling functions of sets, or equivalently, permutation-invariant functions, is a long-standing challenge in machine learning. Deep Sets is a popular method which is known to be a universal approximator for continuous set functions. We provide a theoretical analysis of Deep Sets which shows that this universal approximation property is only guaranteed if the model's latent space is sufficiently high-dimensional. If the latent space is even one dimension lower than necessary, there exist piecewise-affine functions for which Deep Sets performs no better than a naïve constant baseline, as judged by worst-case error. Deep Sets may be viewed as the most efficient incarnation of the Janossy pooling paradigm. We identify this paradigm as encompassing most currently popular set-learning methods. Based on this connection, we discuss the implications of our results for set learning more broadly, and identify some open questions on the universality of Janossy pooling in general.

Neural architecture search (NAS) automates the design of deep neural networks. One of the main challenges in searching complex and non-continuous architectures is to compare the similarity of networks that the conventional Euclidean metric may fail to capture. Optimal transport (OT) is resilient to such complex structure by considering the minimal cost for transporting a network into another. However, the OT is generally not negative definite which may limit its ability to build the positive-definite kernels required in many kernel-dependent frameworks. Building upon tree-Wasserstein (TW), which is a negative definite variant of OT, we develop a novel discrepancy for neural architectures, and demonstrate it within a Gaussian process surrogate model for the sequential NAS settings. Furthermore, we derive a novel parallel NAS, using quality k-determinantal point process on the GP posterior, to select diverse and high-performing architectures from a discrete set of candidates. Empirically, we demonstrate that our TW-based approaches outperform other baselines in both sequential and parallel NAS.

High-dimensional black-box optimisation remains an important yet notoriously challenging problem. Despite the success of Bayesian optimisation methods on continuous domains, domains that are categorical, or that mix continuous and categorical variables, remain challenging. We propose a novel solution—we combine local optimisation with a tailored kernel design, effectively handling high-dimensional categorical and mixed search spaces, whilst retaining sample efficiency. We further derive convergence guarantee for the proposed approach. Finally, we demonstrate empirically that our method outperforms the current baselines on a variety of synthetic and real-world tasks in terms of performance, computational costs, or both.

KL-regularized reinforcement learning from expert demonstrations has proved successful in improving the sample efficiency of deep reinforcement learning algorithms, allowing them to be applied to challenging physical real-world tasks. However, we show that KL-regularized reinforcement learning with behavioral reference policies derived from expert demonstrations can suffer from pathological training dynamics that can lead to slow, unstable, and suboptimal online learning. We show empirically that the pathology occurs for commonly chosen behavioral policy classes and demonstrate its impact on sample efficiency and online policy performance. Finally, we show that the pathology can be remedied by non-parametric behavioral reference policies and that this allows KL-regularized reinforcement learning to significantly outperform state-of-the-art approaches on a variety of challenging locomotion and dexterous hand manipulation tasks.

Graph neural networks, a popular class of models effective in a wide range of graph-based learning tasks, have been shown to be vulnerable to adversarial attacks. While the majority of the literature focuses on such vulnerability in node-level classification tasks, little effort has been dedicated to analysing adversarial attacks on graph-level classification, an important problem with numerous real-life applications such as biochemistry and social network analysis. The few existing methods often require unrealistic setups, such as access to internal information of the victim models, or an impractically-large number of queries. We present a novel Bayesian optimisation-based attack method for graph classification models. Our method is black-box, query-efficient and parsimonious with respect to the perturbation applied. We empirically validate the effectiveness and flexibility of the proposed method on a wide range of graph classification tasks involving varying graph properties, constraints and modes of attack. Finally, we analyse common interpretable patterns behind the adversarial samples produced, which may shed further light on the adversarial robustness of graph classification models.

Accumulating evidence from human-based research has highlighted that the prevalent one-size-fits-all approach for neural and behavioral interventions is inefficient. This approach can benefit one individual, but be ineffective or even detrimental for another. Studying the efficacy of the large range of different parameters for different individuals is costly, time-consuming and requires a large sample size that makes such research impractical and hinders effective interventions. Here an active machine learning technique is presented across participants-personalized Bayesian optimization (pBO)-that searches available parameter combinations to optimize an intervention as a function of an individual's ability. This novel technique was utilized to identify transcranial alternating current stimulation (tACS) frequency and current strength combinations most likely to improve arithmetic performance, based on a subject's baseline arithmetic abilities. The pBO was performed across all subjects tested, building a model of subject performance, capable of recommending parameters for future subjects based on their baseline arithmetic ability. pBO successfully searches, learns, and recommends parameters for an effective neurointervention as supported by behavioral, simulation, and neural data. The application of pBO in human-based research opens up new avenues for personalized and more effective interventions, as well as discoveries of protocols for treatment and translation to other clinical and non-clinical domains.

Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on constrained Gaussian processes and leverage it to build a computationally and data efficient algorithm for state and parameter inference. In an extensive set of experiments, our approach outperforms the current state of the art for parameter inference both in terms of accuracy and computational cost. It also shows promising results for the much more challenging problem of model selection.

We propose Radial Bayesian Neural Networks (BNNs): a variational approximate posterior for BNNs which scales well to large models. Unlike scalable Bayesian deep learning methods like deep ensembles that have discrete support (assign exactly zero probability almost everywhere in weight-space) Radial BNNs maintain full support; letting them act as a prior for continual learning and avoiding the a priori implausibility of discrete support. Our method avoids a sampling problem in mean-field variational inference (MFVI) caused by the so-called ’soap-bubble’ pathology of multivariate Gaussians. We show that, unlike MFVI, Radial BNNs are robust to hyperparameters and can be efficiently applied to challenging real-world tasks without needing ad-hoc tweaks and intensive tuning: on a real-world medical imaging task Radial BNNs outperform MC dropout and deep ensembles.

Bayesian optimization has demonstrated impressive success in finding the optimum input x$\ast$ and output f$\ast$ = f(x$\ast$) = max f(x) of a black-box function f. In some applications, however, the optimum output is known in advance and the goal is to find the corresponding optimum input. Existing work in Bayesian optimization (BO) has not effectively exploited the knowledge of f$\ast$ for optimization. In this paper, we consider a new setting in BO in which the knowledge of the optimum output is available. Our goal is to exploit the knowledge about f$\ast$ to search for the input x$\ast$ efficiently. To achieve this goal, we first transform the Gaussian process surrogate using the information about the optimum output. Then, we propose two acquisition functions, called confidence bound minimization and expected regret minimization, which exploit the knowledge about the optimum output to identify the optimum input more efficient. We show that our approaches work intuitively and quantitatively better performance against standard BO methods. We demonstrate real applications in tuning a deep reinforcement learning algorithm on the CartPole problem and XGBoost on Skin Segmentation dataset in which the optimum values are publicly available.

Efficient optimisation of black-box problems that comprise both continuous and categorical inputs is important, yet poses significant challenges. Current approaches, like one-hot encoding, severely increase the dimension of the search space, while separate modelling of category-specific data is sample-inefficient. Both frameworks are not scalable to practical applications involving multiple categorical variables, each with multiple possible values. We propose a new approach, Continuous and Categorical Bayesian Optimisation (CoCaBO), which combines the strengths of multi-armed bandits and Bayesian optimisation to select values for both categorical and continuous inputs. We model this mixed-type space using a Gaussian Process kernel, designed to allow sharing of information across multiple categorical variables; this allows CoCaBO to leverage all available data efficiently. We extend our method to the batch setting and propose an efficient selection procedure that dynamically balances exploration and exploitation whilst encouraging batch diversity. We demonstrate empirically that our method outperforms existing approaches on both synthetic and real-world optimisation tasks with continuous and categorical inputs.

Achieving the full promise of the Thermodynamic Variational Objective (TVO), a recently proposed variational inference objective that lower-bounds the log evidence via one-dimensional Riemann integration, requires choosing a ``schedule'' of sorted discretization points. This paper introduces a bespoke Gaussian process bandit optimization method for automatically choosing these points. Our approach not only automates their one-time selection, but also dynamically adapts their positions over the course of optimization, leading to improved model learning and inference. We provide theoretical guarantees that our bandit optimization converges to the regret-minimizing choice of integration points. Empirical validation of our algorithm is provided in terms of improved learning and inference in Variational Autoencoders and sigmoid belief networks.

The performance of deep (reinforcement) learning systems crucially depends on the choice of hyperparameters. Their tuning is notoriously expensive, typically requiring an iterative training process to run for numerous steps to convergence. Traditional tuning algorithms only consider the final performance of hyperparameters acquired after many expensive iterations and ignore intermediate information from earlier training steps. In this paper, we present a Bayesian optimization(BO) approach which exploits the iterative structure of learning algorithms for efficient hyperparameter tuning. We propose to learn an evaluation function compressing learning progress at any stage of the training process into a single numeric score according to both training success and stability. Our BO framework is then trade-off the benefit of assessing a hyperparameter setting over additional training steps against their computation cost. We further increase model efficiency by selectively including scores from different training steps for any evaluated hyperparameter set. We demonstrate the efficiency of our algorithm by tuning hyperparameters for the training of deep reinforcement learning agents and convolutional neural networks. Our algorithm outperforms all existing baselines in identifying optimal hyperparameters in minimal time.

Bayesian optimisation has been successfully applied to a variety of reinforcement learning problems. However, the traditional approach for learning optimal policies in simulators does not utilise the opportunity to improve learning by adjusting certain environment variables: state features that are unobservable and randomly determined by the environment in a physical setting but are controllable in a simulator. This article considers the problem of finding a robust policy while taking into account the impact of environment variables. We present Alternating Optimisation and Quadrature (ALOQ), which uses Bayesian optimisation and Bayesian quadrature to address such settings. We also present Transferable ALOQ (TALOQ), for settings where simulator inaccuracies lead to difficulty in transferring the learnt policy to the physical system. We show that our algorithms are robust to the presence of significant rare events, which may not be observable under random sampling but play a substantial role in determining the optimal policy. Experimental results across different domains show that our algorithms learn robust policies efficiently.

We propose a novel, theoretically-grounded, acquisition function for Batch Bayesian Optimization informed by insights from distributionally ambiguous optimization. Our acquisition function is a lower bound on the well-known Expected Improvement function, which requires evaluation of a Gaussian expectation over a multivariate piecewise affine function. Our bound is computed instead by evaluating the best-case expectation over all probability distributions consistent with the same mean and variance as the original Gaussian distribution. Unlike alternative approaches, including Expected Improvement, our proposed acquisition function avoids multi-dimensional integrations entirely, and can be computed exactly - even on large batch sizes - as the solution of a tractable convex optimization problem. Our suggested acquisition function can also be optimized efficiently, since first and second derivative information can be calculated inexpensively as by-products of the acquisition function calculation itself. We derive various novel theorems that ground our work theoretically and we demonstrate superior performance via simple motivating examples, benchmark functions and real-world problems.

Despite growing alarm about machine learning technologies automating jobs, there is little good evidence on what activities can be automated using such technologies. We contribute the first dataset of its kind by surveying over 150 top academics and industry experts in machine learning, robotics and AI, receiving over 4,500 ratings of how automatable specific tasks are today. We present a probabilistic machine learning model to learn the patterns connecting expert estimates of task automatability and the skills, knowledge and abilities required to perform those tasks. Our model infers the automatability of over 2,000 work activities, and we show how automation differs across types of activities and types of occupations. Sensitivity analysis identifies the specific skills, knowledge and abilities of activities that drive higher or lower automatability. We provide quantitative evidence of what is perceived to be automatable using the state-of-the-art in machine learning technology. We consider the societal impacts of these results and of task-level approaches.

Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel, probabilistic model for estimating the drift and diffusion given noisy observations of the underlying stochastic system. Using state-of-the-art adversarial and moment matching inference techniques, we avoid the discretization schemes of classical approaches. This leads to significant improvements in parameter accuracy and robustness given random initial guesses. On four established benchmark systems, we compare the performance of our algorithms to state-of-the-art solutions based on extended Kalman filtering and Gaussian processes.

Batch Bayesian optimisation (BO) has been successfully applied to hyperparameter tuning using parallel computing, but it is wasteful of resources: workers that complete jobs ahead of others are left idle. We address this problem by developing an approach, Penalising Locally for Asynchronous Bayesian Optimisation on K Workers (PLAyBOOK), for asynchronous parallel BO. We demonstrate empirically the efficacy of PLAyBOOK and its variants on synthetic tasks and a real-world problem. We undertake a comparison between synchronous and asynchronous BO, and show that asynchronous BO often outperforms synchronous batch BO in both wall-clock time and sample efficiency.

We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for computationally expensive models. Although previous research has shown that BQ offers sample efficiency superior to Monte Carlo in computing the evidence of an individual model, applying BQ directly to model comparison may waste computation producing an overly-accurate estimate for the evidence of a clearly poor model. We propose an automated and efficient algorithm for computing the most-relevant quantity for model selection: the posterior model probability. Our technique maximizes the mutual information between this quantity and observations of the models’ likelihoods, yielding efficient sample acquisition across disparate model spaces when likelihood observations are limited. Our method produces more-accurate posterior estimates using fewer likelihood evaluations than standard Bayesian quadrature and Monte Carlo estimators, as we demonstrate on synthetic and real-world examples.

Policy gradient methods ignore the potential value of adjusting environment variables: unobservable state features that are randomly determined by the environment in a physical setting, but are controllable in a simulator. This can lead to slow learning, or convergence to suboptimal policies, if the environment variable has a large impact on the transition dynamics. In this paper, we present fingerprint policy optimisation (FPO), which finds a policy that is optimal in expectation across the distribution of environment variables. The central idea is to use Bayesian optimisation (BO) to actively select the distribution of the environment variable that maximises the improvement generated by each iteration of the policy gradient method. To make this BO practical, we contribute two easy-to-compute low-dimensional fingerprints of the current policy. Our experiments show that FPO can efficiently learn policies that are robust to significant rare events, which are unlikely to be observable under random sampling, but are key to learning good policies.

Recent work on the representation of functions on sets has considered the use of summation in a latent space to enforce permutation invariance. In particular, it has been conjectured that the dimension of this latent space may remain fixed as the cardinality of the sets under consideration increases. However, we demonstrate that the analysis leading to this conjecture requires mappings which are highly discontinuous and argue that this is only of limited practical use. Motivated by this observation, we prove that an implementation of this model via continuous mappings (as provided by e.g. neural networks or Gaussian processes) actually imposes a constraint on the dimensionality of the latent space. Practical universal function representation for set inputs can only be achieved with a latent dimension at least the size of the maximum number of input elements.

Accurate on-board capacity estimation is of critical importance in lithium-ion battery applications. Battery charging/discharging often occurs under a constant current load, and hence voltage versus time measurements under this condition may be accessible in practice. This paper presents a data-driven diagnostic technique, Gaussian process regression for in situ capacity estimation (GP-ICE), which estimates battery capacity using voltage measurements over short periods of galvanostatic operation. Unlike previous works, GP-ICE does not rely on interpreting the voltage-time data as incremental capacity (IC) or differential voltage (DV) curves. This overcomes the need to differentiate the voltage-time data (a process that amplifies measurement noise), and the requirement that the range of voltage measurements encompasses the peaks in the IC/DV curves. GP-ICE is applied to two datasets, consisting of 8 and 20 cells, respectively. In each case, within certain voltage ranges, as little as 10 s of galvanostatic operation enables capacity estimates with approximately 2%-3% root-mean-squared error (RMSE).

Bayesian optimisation has been successfully applied to a variety of reinforcement learning problems. However, the traditional approach for learning optimal policies in simulators does not utilise the opportunity to improve learning by adjusting certain environment variables: state features that are unobservable and randomly determined by the environment in a physical setting but are controllable in a simulator. This paper considers the problem of finding a robust policy while taking into account the impact of environment variables. We present Alternating Optimisation and Quadrature (ALOQ), which uses Bayesian optimisation and Bayesian quadrature to address such settings. ALOQ is robust to the presence of significant rare events, which may not be observable under random sampling, but play a substantial role in determining the optimal policy. Experimental results across different domains show that ALOQ can learn more efficiently and robustly than existing methods.

Gradient-based optimization and Markov Chain Monte Carlo sampling can be found at the heart of several machine learning methods. In high-dimensional settings, well-known issues such as slow-mixing, non-convexity and correlations can hinder the algorithms’ efficiency. In order to overcome these difficulties, we propose AdaGeo, a preconditioning framework for adaptively learning the geometry of the parameter space during optimization or sampling. In particular, we use the Gaussian process latent variable model (GP-LVM) to represent a lower-dimensional embedding of the parameters, identifying the underlying Riemannian manifold on which the optimization or sampling is taking place. Samples or optimization steps are consequently proposed based on the geometry of the manifold. We apply our framework to stochastic gradient descent, stochastic gradient Langevin dynamics, and stochastic gradient Riemannian Langevin dynamics, and show performance improvements for both optimization and sampling.

We develop the first Bayesian Optimization algorithm, BLOSSOM, which selects between multiple alternative acquisition functions and traditional local optimization at each step. This is combined with a novel stopping condition based on expected regret. This pairing allows us to obtain the best characteristics of both local and Bayesian optimization, making efficient use of function evaluations while yielding superior convergence to the global minimum on a selection of optimization problems, and also halting optimization once a principled and intuitive stopping condition has been fulfilled.

Information-theoretic Bayesian optimisation techniques have demonstrated state-of-the-art performance in tackling important global optimisation problems. However, current information-theoretic approaches require many approximations in implementation, introduce often-prohibitive computational overhead and limit the choice of kernels available to model the objective. We develop a fast information-theoretic Bayesian Optimisation method, FITBO, that avoids the need for sampling the global minimiser, thus significantly reducing computational overhead. Moreover, in comparison with existing approaches, our method faces fewer constraints on kernel choice and enjoys the merits of dealing with the output space. We demonstrate empirically that FITBO inherits the performance associated with information-theoretic Bayesian optimisation, while being even faster than simpler Bayesian optimisation approaches, such as Expected Improvement.

We present the first treatment of the arc length of the GP with more than a single output dimension. GPs are commonly used for tasks such as trajectory modelling, where path length is a crucial quantity of interest. Previously, only paths in one dimension have been considered, with no theoretical consideration of higher dimensional problems. We fill the gap in the existing literature by deriving the moments of the arc length for a stationary GP with multiple output dimensions. A new method is used to derive the mean of a one-dimensional GP over a finite interval, by considering the distribution of the arc length integrand. This technique is used to derive an approximate distribution over the arc length of a vector valued GP in $\mathbbR^n$ by moment matching the distribution. Numerical simulations confirm our theoretical derivations.

We present GLASSES: Global optimisation with Look-Ahead through Stochastic Simulation and Expected-loss Search. The majority of global optimisation approaches in use are myopic, in only considering the impact of the next function value; the non-myopic approaches that do exist are able to consider only a handful of future evaluations. Our novel algorithm, GLASSES, permits the consideration of dozens of evaluations into the future. This is done by approximating the ideal look-ahead loss function, which is expensive to evaluate, by a cheaper alternative in which the future steps of the algorithm are simulated beforehand. An Expectation Propagation algorithm is used to compute the expected value of the loss. We show that the far-horizon planning thus enabled leads to substantive performance gains in empirical tests.

We introduce a probabilistic model for the factorisation of continuous Poisson process rate functions. Our model can be thought of as a topic model for Poisson point processes in which each point is assigned to one of a set of latent rate functions that are shared across multiple outputs. We show that the model brings a means of incorporating structure in point process inference beyond the state-of-the-art. We derive an efficient variational inference scheme for the model based on sparse Gaussian processes that scales linearly in the number of data points. Finally, we demonstrate, using examples from spatial and temporal statistics, how the model can be used for discovering hidden structure with greater precision than standard frequentist approaches.

The computational and storage complexity of kernel machines presents the primary barrier to their scaling to large, modern, datasets. A common way to tackle the scalability issue is to use the conjugate gradient algorithm, which relieves the constraints on both storage (the kernel matrix need not be stored) and computation (both stochastic gradients and parallelization can be used). Even so, conjugate gradient is not without its own issues: the conditioning of kernel matrices is often such that conjugate gradients will have poor convergence in practice. Preconditioning is a common approach to alleviating this issue. Here we propose preconditioned conjugate gradients for kernel machines, and develop a broad range of preconditioners particularly useful for kernel matrices. We describe a scalable approach to both solving kernel machines and learning their hyperparameters. We show this approach is exact in the limit of iterations and outperforms state-of-the-art approximations for a given computational budget.

We present the first general purpose framework for marginal maximum a posteriori estimation of probabilistic program variables. By using a series of code transformations, the evidence of any probabilistic program, and therefore of any graphical model, can be optimized with respect to an arbitrary subset of its sampled variables. To carry out this optimization, we develop the first Bayesian optimization package to directly exploit the source code of its target, leading to innovations in problem-independent hyperpriors, unbounded optimization, and implicit constraint satisfaction; delivering significant performance improvements over prominent existing packages. We present applications of our method to a number of tasks including engineering design and parameter optimization.

We present the first fully variational Bayesian inference scheme for continuous Gaussian-process-modulated Poisson processes. Such point processes are used in a variety of domains, including neuroscience, geo-statistics and astronomy, but their use is hindered by the computational cost of existing inference schemes. Our scheme: requires no discretisation of the domain; scales linearly in the number of observed events; and is many orders of magnitude faster than previous sampling based approaches. The resulting algorithm is shown to outperform standard methods on synthetic examples, coal mining disaster data and in the prediction of Malaria incidences in Kenya.

There is renewed interest in formulating integration as an inference problem, motivated by obtaining a full distribution over numerical error that can be propagated through subsequent computation. Current methods, such as Bayesian Quadrature, demonstrate impressive empirical performance but lack theoretical analysis. An important challenge is to reconcile these probabilistic integrators with rigorous convergence guarantees. In this paper, we present the first probabilistic integrator that admits such theoretical treatment, called Frank-Wolfe Bayesian Quadrature (FWBQ). Under FWBQ, convergence to the true value of the integral is shown to be exponential and posterior contraction rates are proven to be superexponential. In simulations, FWBQ is competitive with state-of-the-art methods and out-performs alternatives based on Frank-Wolfe optimisation. Our approach is applied to successfully quantify numerical error in the solution to a challenging model choice problem in cellular biology.

We present a system and study of personalized energy-related recommendation. AgentSwitch utilizes electricity usage data collected from users' households over a period of time to realize a range of smart energy-related recommendations on energy tariffs, load detection and usage shifting. The web service is driven by a third party real-time energy tariff API (uSwitch), an energy data store, a set of algorithms for usage prediction, and appliance-level load disaggregation. We present the system design and user evaluation consisting of interviews and interface walkthroughs. We recruited participants from a previous study during which three months of their household's energy use was recorded to evaluate personalized recommendations in AgentSwitch. Our contributions are a) a systems architecture for personalized energy services; and b) findings from the evaluation that reveal challenges in designing energy-related recommender systems. In response to the challenges we formulate design recommendations to mitigate barriers to switching tariffs, to incentivize load shifting, and to automate energy management.

Many signals of interest are corrupted by faults of anunknown type. We propose an approach that uses Gaus-sian processes and a general “fault bucket” to capturea priori uncharacterised faults, along with an approxi-mate method for marginalising the potential faultinessof all observations. This gives rise to an efficient, flexible algorithm for the detection and automatic correction of faults. Our method is deployed in the domain of water monitoring and management, where it is able to solve several fault detection, correction, and prediction problems. The method works well despite the fact that the data is plagued with numerous difficulties, including missing observations, multiple discontinuities, nonlinearity and many unanticipated types of fault.

Numerical integration is an key component of many problems in scientific computing, statistical modelling, and machine learning. Bayesian Quadrature is a model-based method for numerical integration which, relative to standard Monte Carlo methods, offers increased sample efficiency and a more robust estimate of the uncertainty in the estimated integral. We propose a novel Bayesian Quadrature approach for numerical integration when the integrand is non-negative, such as the case of computing the marginal likelihood, predictive distribution, or normalising constant of a probabilistic model. Our approach approximately marginalises the quadrature model's hyperparameters in closed form, and introduces an active learning scheme to optimally select function evaluations, as opposed to using Monte Carlo samples. We demonstrate our method on both a number of synthetic benchmarks and a real scientific problem from astronomy.

In this article, we consider the problem faced by a sensor network operator who must infer, in real time, the value of some environmental parameter that is being monitored at discrete points in space and time by a sensor network. We describe a powerful and generic approach built upon an efficient multi-output Gaussian process that facilitates this information acquisition and processing. Our algorithm allows effective inference even with minimal domain knowledge, and we further introduce a formulation of Bayesian Monte Carlo to permit the principled management of the hyperparameters introduced by our flexible models. We demonstrate how our methods can be applied in cases where the data is delayed, intermittently missing, censored, and/or correlated. We validate our approach using data collected from three networks of weather sensors and show that it yields better inference performance than both conventional independent Gaussian processes and the Kalman filter. Finally, we show that our formalism efficiently reuses previous computations by following an online update procedure as new data sequentially arrives, and that this results in a four-fold increase in computational speed in the largest cases considered.

We describe a Bayesian formalism for the intelligent selection of observations from sensor networks that may intermittently undergo faults or changepoints. Such active data selection is performed with the goal of taking as few observations as necessary in order to maintain a reasonable level of uncertainty about the variables of interest. The presence of faults/changepoints is not always obvious and therefore our algorithm must first detect their occurrence. Having done so, our selection of observations must be appropriately altered. Faults corrupt our observations, reducing their impact; changepoints (abrupt changes in the characteristics of data) may require the transition to an entirely different sampling schedule. Our solution is to employ a Gaussian process formalism that allows for sequential time-series prediction about variables of interest along with a decision theoretic approach to the problem of selecting observations.

We consider the problem of selecting an optimal set of sensors, as determined, for example, by the predictive accuracy of the resulting sensor network. Given an underlying metric between pairs of set elements, we introduce a natural metric between sets of sensors for this task. Using this metric, we can construct covariance functions over sets, and thereby perform Gaussian process inference over a function whose domain is a power set. If the function has additional inputs, our covariances can be readily extended to incorporate them---allowing us to consider, for example, functions over both sets and time. These functions can then be optimized using Gaussian process global optimization (GPGO). We use the root mean squared error (RMSE) of the predictions made using a set of sensors at a particular time as an example of such a function to be optimized; the optimal point specifies the best choice of sensor locations. We demonstrate the resulting method by dynamically selecting the best subset of a given set of weather sensors for the prediction of the air temperature across the United Kingdom.

We introduce a new sequential algorithm for making robust predictions in the presence of changepoints. Unlike previous approaches, which focus on the problem of detecting and locating changepoints, our algorithm focuses on the problem of making predictions even when such changes might be present. We introduce nonstationary covariance functions to be used in Gaussian process prediction that model such changes, and then proceed to demonstrate how to effectively manage the hyperparameters associated with those covariance functions. We further introduce covariance functions to be used in situations where our observation model undergoes changes, as is the case for sensor faults. By using Bayesian quadrature, we can integrate out the hyperparameters, allowing us to calculate the full marginal predictive distribution. Furthermore, if desired, the posterior distribution over putative changepoint locations can be calculated as a natural byproduct of our prediction algorithm.

We introduce a new sequential algorithm for making robust predictions in the presence of changepoints. Unlike previous approaches, which focus on the problem of detecting and locating changepoints, our algorithm focuses on the problem of making predictions even when such changes might be present. We introduce nonstationary covariance functions to be used in Gaussian process prediction that model such changes, then proceed to demonstrate how to effectively manage the hyperparameters associated with those covariance functions. By using Bayesian quadrature, we can integrate out the hyperparameters, allowing us to calculate the marginal predictive distribution. Furthermore, if desired, the posterior distribution over putative changepoint locations can be calculated as a natural byproduct of our prediction algorithm.

In this paper, we describe a novel, computationally efficient algorithm that facilitates the autonomous acquisition of readings from sensor networks (deciding when and which sensor to acquire readings from at any time), and which can, with minimal domain knowledge, perform a range of information processing tasks including modelling the accuracy of the sensor readings, predicting the value of missing sensor readings, and predicting how the monitored environmental variables will evolve into the future. Our motivating scenario is the need to provide situational awareness support to first responders at the scene of a large scale incident, and to this end, we describe a novel iterative formulation of a multi-output Gaussian process that can build and exploit a probabilistic model of the environmental variables being measured (including the correlations and delays that exist between them). We validate our approach using data collected from a network of weather sensors located on the south coast of England.