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Michael A Osborne

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13 papers

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NeurIPS Conference 2025 Conference Paper

Just One Layer Norm Guarantees Stable Extrapolation

Juliusz Ziomek
George Whittle
Michael A Osborne

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.

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RLC Conference 2025 Conference Paper

PAC Apprenticeship Learning with Bayesian Active Inverse Reinforcement Learning

Ondrej Bajgar
Dewi Sid William Gould
Jonathon Liu
Alessandro Abate
Konstantinos Gatsis
Michael A Osborne

As AI systems become increasingly autonomous, reliably aligning their decision-making with human preferences is essential. Inverse reinforcement learning (IRL) offers a promising approach to infer preferences from demonstrations. These preferences can then be used to produce an apprentice policy that performs well on the demonstrated task. However, in domains like autonomous driving or robotics, where errors can have serious consequences, we need not just good average performance but reliable policies with formal guarantees. But obtaining sufficient human demonstrations for reliability guarantees can be costly. *Active* IRL addresses this challenge by strategically selecting the most informative scenarios for human demonstration. We introduce PAC-EIG, an information-theoretic acquisition function that directly targets probably-approximately-correct (PAC) guarantees for the learned policy -- providing the first such theoretical guarantee for active IRL with imperfect expert demonstrations. Our method maximizes information gain about immediate regret, efficiently identifying which states require further demonstration to ensure reliable apprentice behaviour. We also present an alternative method for scenarios where learning the reward itself is the primary objective. We prove convergence bounds, illustrate failure modes of prior heuristic methods, and demonstrate our approach experimentally.

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RLJ Journal 2025 Journal Article

PAC Apprenticeship Learning with Bayesian Active Inverse Reinforcement Learning

Ondrej Bajgar
Dewi Sid William Gould
Jonathon Liu
Alessandro Abate
Konstantinos Gatsis
Michael A Osborne

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NeurIPS Conference 2025 Conference Paper

Scalable Valuation of Human Feedback through Provably Robust Model Alignment

Masahiro Fujisawa
Masaki Adachi
Michael A Osborne

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.

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NeurIPS Conference 2023 Conference Paper

Bayesian Optimisation of Functions on Graphs

Xingchen Wan
Pierre Osselin
Henry Kenlay
Binxin Ru
Michael A Osborne
Xiaowen Dong

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.

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TMLR Journal 2023 Journal Article

Bayesian Quadrature for Neural Ensemble Search

Saad Hamid
Xingchen Wan
Martin Jørgensen
Binxin Ru
Michael A Osborne

Ensembling can improve the performance of Neural Networks, but existing approaches struggle when the architecture likelihood surface has dispersed, narrow peaks. Furthermore, existing methods construct equally weighted ensembles, and this is likely to be vulnerable to the failure modes of the weaker architectures. By viewing ensembling as approximately marginalising over architectures we construct ensembles using the tools of Bayesian Quadrature -- tools which are well suited to the exploration of likelihood surfaces with dispersed, narrow peaks. Additionally, the resulting ensembles consist of architectures weighted commensurate with their performance. We show empirically -- in terms of test likelihood, accuracy, and expected calibration error -- that our method outperforms state-of-the-art baselines, and verify via ablation studies that its components do so independently.

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TMLR Journal 2023 Journal Article

Challenges and Opportunities in Offline Reinforcement Learning from Visual Observations

Cong Lu
Philip J. Ball
Tim G. J. Rudner
Jack Parker-Holder
Michael A Osborne
Yee Whye Teh

Offline reinforcement learning has shown great promise in leveraging large pre-collected datasets for policy learning, allowing agents to forgo often-expensive online data collection. However, offline reinforcement learning from visual observations with continuous action spaces remains under-explored, with a limited understanding of the key challenges in this complex domain. In this paper, we establish simple baselines for continuous control in the visual domain and introduce a suite of benchmarking tasks for offline reinforcement learning from visual observations designed to better represent the data distributions present in real-world offline RL problems and guided by a set of desiderata for offline RL from visual observations, including robustness to visual distractions and visually identifiable changes in dynamics. Using this suite of benchmarking tasks, we show that simple modifications to two popular vision-based online reinforcement learning algorithms, DreamerV2 and DrQ-v2, suffice to outperform existing offline RL methods and establish competitive baselines for continuous control in the visual domain. We rigorously evaluate these algorithms and perform an empirical evaluation of the differences between state-of-the-art model-based and model-free offline RL methods for continuous control from visual observations. All code and data used in this evaluation are open-sourced to facilitate progress in this domain.

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NeurIPS Conference 2022 Conference Paper

Bayesian Optimization over Discrete and Mixed Spaces via Probabilistic Reparameterization

Samuel Daulton
Xingchen Wan
David Eriksson
Maximilian Balandat
Michael A Osborne
Eytan Bakshy

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.

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NeurIPS Conference 2022 Conference Paper

Bezier Gaussian Processes for Tall and Wide Data

Martin Jørgensen
Michael A Osborne

Modern approximations to Gaussian processes are suitable for tall data'', with a cost that scales well in the number of observations, but under-performs on wide 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.

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NeurIPS Conference 2022 Conference Paper

Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombination

Masaki Adachi
Satoshi Hayakawa
Martin Jørgensen
Harald Oberhauser
Michael A Osborne

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.

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NeurIPS Conference 2022 Conference Paper

Log-Linear-Time Gaussian Processes Using Binary Tree Kernels

Michael K. Cohen
Samuel Daulton
Michael A Osborne

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.

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NeurIPS Conference 2021 Conference Paper

Adversarial Attacks on Graph Classifiers via Bayesian Optimisation

Xingchen Wan
Henry Kenlay
Robin Ru
Arno Blaas
Michael A Osborne
Xiaowen Dong

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.

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NeurIPS Conference 2021 Conference Paper

On Pathologies in KL-Regularized Reinforcement Learning from Expert Demonstrations

Tim G. J. Rudner
Cong Lu
Michael A Osborne
Yarin Gal
Yee Teh

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.

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