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Identifying key patterns of tactics implemented by rival teams, and developing effective responses, lies at the heart of modern football. However, doing so algorithmically remains an open research challenge. To address this unmet need, we propose TacticAI, an AI football tactics assistant developed and evaluated in close collaboration with domain experts from Liverpool FC. We focus on analysing corner kicks, as they offer coaches the most direct opportunities for interventions and improvements. TacticAI incorporates both a predictive and a generative component, allowing the coaches to effectively sample and explore alternative player setups for each corner kick routine and to select those with the highest predicted likelihood of success. We validate TacticAI on a number of relevant benchmark tasks: predicting receivers and shot attempts and recommending player position adjustments. The utility of TacticAI is validated by a qualitative study conducted with football domain experts at Liverpool FC. We show that TacticAI’s model suggestions are not only indistinguishable from real tactics, but also favoured over existing tactics 90% of the time, and that TacticAI offers an effective corner kick retrieval system. TacticAI achieves these results despite the limited availability of gold-standard data, achieving data efficiency through geometric deep learning. In modern football games, data-driven analysis serves as a key driver in determining tactics. Wang, Veličković, Hennes et al. develop a geometric deep learning algorithm, named TacticAI, to solve high-dimensional learning tasks over corner kicks and suggest tactics favoured over existing ones 90% of the time.

In multiagent worlds, several decision-making individuals interact while adhering to the dynamics constraints imposed by the environment. These interactions, combined with the potential stochasticity of the agents’ dynamic behaviors, make such systems complex and interesting to study from a decision-making perspective. Significant research has been conducted on learning models for forward-direction estimation of agent behaviors, for example, pedestrian predictions used for collision-avoidance in self-driving cars. In many settings, only sporadic observations of agents may be available in a given trajectory sequence. In football, subsets of players may come in and out of view of broadcast video footage, while unobserved players continue to interact off-screen. In this paper, we study the problem of multiagent time-series imputation in the context of human football play, where available past and future observations of subsets of agents are used to estimate missing observations for other agents. Our approach, called the Graph Imputer , uses past and future information in combination with graph networks and variational autoencoders to enable learning of a distribution of imputed trajectories. We demonstrate our approach on multiagent settings involving players that are partially-observable, using the Graph Imputer to predict the behaviors of off-screen players. To quantitatively evaluate the approach, we conduct experiments on football matches with ground truth trajectory data, using a camera module to simulate the off-screen player state estimation setting. We subsequently use our approach for downstream football analytics under partial observability using the well-established framework of pitch control, which traditionally relies on fully observed data. We illustrate that our method outperforms several state-of-the-art approaches, including those hand-crafted for football, across all considered metrics.

A good model of object shape is essential in applications such as segmentation, detection, inpainting and graphics. For example, when performing segmentation, local constraints on the shapes can help where object boundaries are noisy or unclear, and global constraints can resolve ambiguities where background clutter looks similar to parts of the objects. In general, the stronger the model of shape, the more performance is improved. In this paper, we use a type of deep Boltzmann machine (Salakhutdinov and Hinton, International Conference on Artificial Intelligence and Statistics, 2009 ) that we call a Shape Boltzmann Machine (SBM) for the task of modeling foreground/background (binary) and parts-based (categorical) shape images. We show that the SBM characterizes a strong model of shape, in that samples from the model look realistic and it can generalize to generate samples that differ from training examples. We find that the SBM learns distributions that are qualitatively and quantitatively better than existing models for this task.

The rapid progress in artificial intelligence (AI) and machine learning has opened unprecedented analytics possibilities in various team and individual sports, including baseball, basketball, and tennis. More recently, AI techniques have been applied to football, due to a huge increase in data collection by professional teams, increased computational power, and advances in machine learning, with the goal of better addressing new scientific challenges involved in the analysis of both individual players’ and coordinated teams’ behaviors. The research challenges associated with predictive and prescriptive football analytics require new developments and progress at the intersection of statistical learning, game theory, and computer vision. In this paper, we provide an overarching perspective highlighting how the combination of these fields, in particular, forms a unique microcosm for AI research, while offering mutual benefits for professional teams, spectators, and broadcasters in the years to come. We illustrate that this duality makes football analytics a game changer of tremendous value, in terms of not only changing the game of football itself, but also in terms of what this domain can mean for the field of AI. We review the state-of-the-art and exemplify the types of analysis enabled by combining the aforementioned fields, including illustrative examples of counterfactual analysis using predictive models, and the combination of game-theoretic analysis of penalty kicks with statistical learning of player attributes. We conclude by highlighting envisioned downstream impacts, including possibilities for extensions to other sports (real and virtual).

Imitation learning methods seek to learn from an expert either through behavioral cloning (BC) of the policy or inverse reinforcement learning (IRL) of the reward. Such methods enable agents to learn complex tasks from humans that are difficult to capture with hand-designed reward functions. Choosing BC or IRL for imitation depends on the quality and state-action coverage of the demonstrations, as well as additional access to the Markov decision process. Hybrid strategies that combine BC and IRL are not common, as initial policy optimization against inaccurate rewards diminishes the benefit of pretraining the policy with BC. This work derives an imitation method that captures the strengths of both BC and IRL. In the entropy-regularized ('soft') reinforcement learning setting, we show that the behaviour-cloned policy can be used as both a shaped reward and a critic hypothesis space by inverting the regularized policy update. This coherency facilitates fine-tuning cloned policies using the reward estimate and additional interactions with the environment. This approach conveniently achieves imitation learning through initial behaviour cloning, followed by refinement via RL with online or offline data sources. The simplicity of the approach enables graceful scaling to high-dimensional and vision-based tasks, with stable learning and minimal hyperparameter tuning, in contrast to adversarial approaches. For the open-source implementation and simulation results, see https://joemwatson.github.io/csil/.

Natural images arise from complicated processes involving many factors of variation. They reflect the wealth of shapes and appearances of objects in our three-dimensional world, but they are also affected by factors such as distortions due to perspective, occlusions, and illumination, giving rise to structure with regularities at many different levels. Prior knowledge about these regularities and suitable representations that allow efficient reasoning about the properties of a visual scene are important for many image processing and computer vision tasks. This thesis focuses on models of image structure at intermediate levels of complexity as required, for instance, for image inpainting or segmentation. It aims at developing generative, probabilistic models of this kind of structure, and, in particular, at devising strategies for learning such models in a largely unsupervised manner from data. One hallmark of natural images is that they can often be decomposed into regions with very different visual characteristics. The main approach of this thesis is therefore to represent images in terms of regions that are characterized by their shapes and appearances, and an image is then composed from many such regions. We explore approaches to learn about the appearance of regions, to learn about region shapes, and ways to combine several regions to form a full image. To achieve this goal, we make use of some ideas for unsupervised learning developed in the literature on models of low-level image structure and in the “deep learning” literature. These models are used as building blocks of more structured model formulations that incorporate additional prior knowledge of how images are formed. The thesis makes the following contributions: Firstly, we investigate a popular, MRF based prior of natural image structure, the Field-of Experts, with respect to its ability to model image textures, and propose an extended formulation that is considerably more successful at this task. This formulation gives rise to a fully parametric, translation-invariant probabilistic generative model of image textures. We illustrate how this model can be used as a component of a more comprehensive model of images comprising multiple textured regions. Secondly, we develop a model of region shape. This work is an extension of the “Masked Restricted Boltzmann Machine” proposed by Le Roux et al. (2011) and it allows explicit reasoning about the independent shapes and relative depths of occluding objects. We develop an inference and unsupervised learning scheme and demonstrate how this shape model, in combination with the masked RBM gives rise to a good model of natural image patches. Finally, we demonstrate how this model of region shape can be extended to model shapes in large images. The result is a generative model of large images which are formed by composition from many small, partially overlapping and occluding objects.

Normal-form games (NFGs) are the fundamental model of strategic interaction. We study their representation using neural networks. We describe the inherent equivariance of NFGs -- any permutation of strategies describes an equivalent game -- as well as the challenges this poses for representation learning. We then propose the NfgTransformer architecture that leverages this equivariance, leading to state-of-the-art performance in a range of game-theoretic tasks including equilibrium-solving, deviation gain estimation and ranking, with a common approach to NFG representation. We show that the resulting model is interpretable and versatile, paving the way towards deep learning systems capable of game-theoretic reasoning when interacting with humans and with each other.

We present a simple, yet powerful data-augmentation technique to enable data-efficient learning from parametric experts for reinforcement and imitation learning. We focus on what we call the policy cloning setting, in which we use online or offline queries of an expert or expert policy to inform the behavior of a student policy. This setting arises naturally in a number of problems, for instance as variants of behavior cloning, or as a component of other algorithms such as DAGGER, policy distillation or KL-regularized RL. Our approach, augmented policy cloning (APC), uses synthetic states to induce feedback-sensitivity in a region around sampled trajectories, thus dramatically reducing the environment interactions required for successful cloning of the expert. We achieve highly data-efficient transfer of behavior from an expert to a student policy for high-degrees-of-freedom control problems. We demonstrate the benefit of our method in the context of several existing and widely used algorithms that include policy cloning as a constituent part. Moreover, we highlight the benefits of our approach in two practically relevant settings (a) expert compression, i.e. transfer to a student with fewer parameters; and (b) transfer from privileged experts, i.e. where the expert has a different observation space than the student, usually including access to privileged information.

Contemporary artificial intelligence systems exhibit rapidly growing abilities accompanied by the growth of required resources, expansive datasets and corresponding investments into computing infrastructure. Although earlier successes predominantly focus on constrained settings, recent strides in fundamental research and applications aspire to create increasingly general systems. This evolving landscape presents a dual panorama of opportunities and challenges in refining the generalisation and transfer of knowledge - the extraction from existing sources and adaptation as a comprehensive foundation for tackling new problems. Within the domain of reinforcement learning (RL), the representation of knowledge manifests through various modalities, including dynamics and reward models, value functions, policies, and the original data. This taxonomy systematically targets these modalities and frames its discussion based on their inherent properties and alignment with different objectives and mechanisms for transfer. Where possible, we aim to provide coarse guidance delineating approaches which address requirements such as limiting environment interactions, maximising computational efficiency, and enhancing generalisation across varying axes of change. Finally, we analyse reasons contributing to the prevalence or scarcity of specific forms of transfer, the inherent potential behind pushing these frontiers, and underscore the significance of transitioning from designed to learned transfer.