Each split is entirely unique, and no labyrinth appears more than once in4 the entire dataset, regardless of its split. Each entry consists of five pieces of information:5 obs: the path to the image representation for that state;6 actions: the integer action performed for that solution in that state;7 rewards: the float reward received for that action in that state;8 episode_starts: the boolean status that states if it is the first state in an episode; and9 info: the textual information required to load the same labyrinth structure if needed.10 We provide images in each dataset since we believe that visual information is more useful to the11 imitation learning agent, and if a vector representation is needed, the info parameter allows researchers12 to load the same structure and the actions enables the recreation of the dataset in its vector format.13 Each observation is an image of size 600 600 3. Although each baseline trained in this work14 uses a 64 64 3input, we thought that providing a bigger image would benefit models requiring15 downsizing (e.g., the walls will not disappear during resizing).

Imitation learning benchmarks often lack sufficient variation between training and evaluation, limiting meaningful generalisation assessment. We introduce Labyrinth, a benchmarking environment designed to test generalisation with precise control over structure, start and goal positions, and task complexity. It enables verifiably distinct training, evaluation, and test settings. Labyrinth provides a discrete, fully observable state space and known optimal actions, supporting interpretability and fine-grained evaluation. Its flexible setup allows targeted testing of generalisation factors and includes variants like partial observability, key-and-door tasks, and ice-floor hazards. By enabling controlled, reproducible experiments, Labyrinth advances the evaluation of generalisation in imitation learning and provides a valuable tool for developing more robust agents.

In the zero-shot policy transfer setting in reinforcement learning, the goal is to train an agent on a fixed set of training environments so that it can generalise to similar, but unseen, testing environments. Previous work has shown that policy distillation after training can sometimes produce a policy that outperforms the original in the testing environments. However, it is not yet entirely clear why that is, or what data should be used to distil the policy. In this paper, we prove, under certain assumptions, a generalisation bound for policy distillation after training. The theory provides two practical insights: for improved generalisation, you should 1) train an ensemble of distilled policies, and 2) distil it on as much data from the training environments as possible. We empirically verify that these insights hold in more general settings, when the assumptions required for the theory no longer hold. Finally, we demonstrate that an ensemble of policies distilled on a diverse dataset can generalise significantly better than the original agent.

Reinforcement learning from human feedback usually models preferences using a reward function that does not distinguish between people. We argue that this is unlikely to be a good design choice in contexts with high potential for disagreement, like in the training of large language models. We formalise and analyse the problem of learning a reward model that can be specialised to a user. Using the principle of empirical risk minimisation, we derive a probably approximately correct (PAC) bound showing the dependency of the approximation error on the number of training examples, as usual, and also on the number of human raters who provided feedback on them. Based on our theoretical findings, we discuss how to best collect pairwise preference data and argue that adaptive reward models should be beneficial when there is considerable disagreement among users.

Imitation learning benchmarks often lack sufficient variation between training and evaluation, limiting meaningful generalisation assessment. We introduce Labyrinth, a benchmarking environment designed to test generalisation with precise control over structure, start and goal positions, and task complexity.It enables verifiably distinct training, evaluation, and test settings.Labyrinth provides a discrete, fully observable state space and known optimal actions, supporting interpretability and fine-grained evaluation.Its flexible setup allows targeted testing of generalisation factors and includes variants like partial observability, key-and-door tasks, and ice-floor hazards.By enabling controlled, reproducible experiments, Labyrinth advances the evaluation of generalisation in imitation learning and provides a valuable tool for developing more robust agents.

In the zero-shot policy transfer setting in reinforcement learning, the goal is to train an agent on a fixed set of training environments so that it can generalise to similar, but unseen, testing environments. Previous work has shown that policy distillation after training can sometimes produce a policy that outperforms the original in the testing environments. However, it is not yet entirely clear why that is, or what data should be used to distil the policy. In this paper, we prove, under certain assumptions, a generalisation bound for policy distillation after training. The theory provides two practical insights: for improved generalisation, you should 1) train an ensemble of distilled policies, and 2) distil it on as much data from the training environments as possible. We empirically verify that these insights hold in more general settings, when the assumptions required for the theory no longer hold. Finally, we demonstrate that an ensemble of policies distilled on a diverse dataset can generalise significantly better than the original agent.

Physics-informed machine learning (PIML) integrates mechanistic knowledge, typically in the form of partial differential equations (PDE), into data-driven models. Despite strong empirical performance, its statistical generalisation properties remain poorly understood, particularly in the regression setting with unbounded losses. Existing analyses rely on approximation or stability arguments and do not fully capture how physical structure influences generalisation from finite data. In this work, we develop a PAC-Bayesian framework for PIML that provides high-probability generalisation guarantees in the presence of unbounded losses. We adopt a multi-task perspective that jointly treats data fidelity, PDE residuals, initial and boundary conditions, avoiding the looseness induced by standard union-bound approaches. Our analysis leverages the structure of physics-informed objectives to derive novel bounds where the complexity scales with input-gradient norms of the losses, revealing a direct link between physical regularity and generalisation. We instantiate this framework under Sobolev and Poincaré-type assumptions, yielding two classes of bounds that trade off statistical complexity and smoothness in different regimes. Building on these results, we propose a self-bounding-aware learning algorithm that directly optimises tractable surrogates of the derived bounds, along with a practical procedure to estimate the associated constants in realistic settings. Empirical evaluations on standard PDE benchmarks demonstrate that our bounds are non-vacuous, significantly tighter than union-bound baselines, and can be effectively minimised during training. Overall, our results provide a principled statistical foundation for the generalisation of physics-informed models.

Generative neural networks learn how to produce highly realistic images from a large, but finite number of examples - or do they simply memorise their training set? To settle this question, Kadkhodaie, Guth, Simoncelli and Mallat (ICLR '24) trained diffusion models independently on disjoint subsets of a dataset and showed that they converge to nearly the same density when the number of training images is large enough. This result raises two basic questions: how much data do you need for convergence, and what does convergence capture about learning the data distribution? Here, we address these questions by providing an exact analytical characterisation of the transition from memorisation to generalisation in linear generative models. We find that these models memorise at small load, while convergence emerges continuously when the number of samples is linear in the input dimension. Strikingly, we find that convergence is insensitive to recovery of the principal latent factors of the data, which are recovered in a sharp transition. After extending our approach to data with power-law spectra, we find the same distinction between convergence and latent recovery in our experiments with convolutional denoisers and in the data of Kadkhodaie et al. We thus show that generalisation in generative models decomposes into at least two distinct objectives: matching the bulk of the data distribution and recovering the principal latent factors. These objectives correspond to two different distances between true and learnt data distribution, and only the first one is captured by convergence.

It is a commonly held belief that enforcing invariance improves generalisation. Although this approach enjoys widespread popularity, it is only very recently that a rigorous theoretical demonstration of this benefit has been established. In this work we build on the function space perspective of Elesedy and Zaidi [8] to derive a strictly non-zero generalisation benefit of incorporating invariance in kernel ridge regression when the target is invariant to the action of a compact group. We study invariance enforced by feature averaging and find that generalisation is governed by a notion of effective dimension that arises from the interplay between the kernel and the group. In building towards this result, we find that the action of the group induces an orthogonal decomposition of both the reproducing kernel Hilbert space and its kernel, which may be of interest in its own right.

Multi-agent reinforcement learning (MARL) has emerged as a useful approach to solving decentralised decision-making problems at scale. Research in the field has been growing steadily with many breakthrough algorithms proposed in recent years. In this work, we take a closer look at this rapid development with a focus on evaluation methodologies employed across a large body of research in cooperative MARL. By conducting a detailed meta-analysis of prior work, spanning 75 papers accepted for publication from 2016 to 2022, we bring to light worrying trends that put into question the true rate of progress. We further consider these trends in a wider context and take inspiration from single-agent RL literature on similar issues with recommendations that remain applicable to MARL. Combining these recommendations, with novel insights from our analysis, we propose a standardised performance evaluation protocol for cooperative MARL. We argue that such a standard protocol, if widely adopted, would greatly improve the validity and credibility of future research, make replication and reproducibility easier, as well as improve the ability of the field to accurately gauge the rate of progress over time by being able to make sound comparisons across different works. Finally, we release our meta-analysis data publicly on our project website for future research on evaluation 3 accompanied by our open-source evaluation tools repository4.