Understanding agent behaviour in Multi-Agent Systems (MAS) is an important problem in domains such as autonomous driving, disaster response, and sports analytics. Existing MAS problems typically use uniform timesteps with observations for all agents. In this work, we analyse the problem of agent location imputation, specifically posed in environments with non-uniform timesteps and limited agent observability (~95% missing values). Our approach uses Long Short-Term Memory and Graph Neural Network components to learn temporal and inter-agent patterns to predict the location of all agents at every timestep. We apply this to the domain of football (soccer) by imputing the location of all players in a game from sparse event data (e.g., shots and passes). Our model estimates player locations to within ~6.9m; a ~62% reduction in error from the best performing baseline. This approach facilitates downstream analysis tasks such as player physical metrics, player coverage, and team pitch control. Existing solutions to these tasks often require optical tracking data, which is expensive to obtain and only available to elite clubs. By imputing player locations from easy to obtain event data, we increase the accessibility of downstream tasks.

翻译：多智能体系统（MAS）中理解智能体行为是自动驾驶、灾难响应和体育分析等领域的重要问题。现有MAS问题通常采用均匀时间步长且能观测所有智能体的设置。本研究针对非均匀时间步长且智能体观测受限（约95%缺失值）的环境，分析智能体位置插补问题。我们的方法采用长短期记忆网络和图神经网络组件，通过学习时间模式及智能体间模式，预测每个时间步所有智能体的位置。我们将该方法应用于足球领域，通过稀疏事件数据（如射门和传球）插补比赛中所有运动员的位置。模型对运动员位置的估计误差控制在约6.9米内，较最优基线模型误差降低约62%。该方法可支持运动员身体指标、运动员覆盖范围及球队控球区域等下游分析任务。现有解决方案通常需要光学跟踪数据，这类数据获取成本高昂且仅限精英俱乐部使用。通过从易获取的事件数据中插补运动员位置，我们提高了下游任务的可及性。