DYNAMIC RELATIONAL INFERENCE IN MULTI-AGENT TRAJECTORIES

Abstract

Unsupervised learning of interactions from multi-agent trajectories has broad applications in physics, vision and robotics. However, existing neural relational inference works are limited to static relations. In this paper, we consider a more general setting of dynamic relational inference where interactions change over time. We propose DYnamic multi-Agent Relational Inference (DYARI) model, a deep generative model that can reason about dynamic relations. Using a simulated physics system, we study various dynamic relation scenarios, including periodic and additive dynamics. We perform comprehensive study on the trade-off between dynamic and inference period, the impact of training scheme, and model architecture on dynamic relational inference accuracy. We also showcase an application of our model to infer coordination and competition patterns from real-world multi-agent basketball trajectories.

1. INTRODUCTION

Particles, friends, and teams are multi-agent relations at different scales. Learning multi-agent interactions is essential to our understanding of the structures and dynamics underlying many systems. Practical examples include understanding social dynamics among pedestrians (Alahi et al., 2016) , learning communication protocols in traffic (Sukhbaatar et al., 2016; Lowe et al., 2017) and predicting physical interactions of particles (Mrowca et al., 2018; Li et al., 2018; Sanchez-Gonzalez et al., 2020) . Most existing work on modeling relations assume the interactions are observed and train the models with supervised learning. For multi-agent trajectories, the interactions are hidden and thus need to be inferred from data in an unsupervised fashion. While one could impose an interaction graph structure (Battaglia et al., 2016) , it is difficult to find the correct structure as the search space is very large (Grosse et al., 2012) . The search task is computationally expensive and the resulting model can potentially suffer from the model misspecification issue (Koopmans & Reiersol, 1950) .

Neural Relational Inference for Interacting Systems

Thomas Kipf * 1 Ethan Fetaya * 2 3 Kuan-Chieh Wang 2 3 Max Welling 1 4 Richard Zemel 2 3 4

Abstract

Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's constituent parts. In this work, we introduce the neural relational inference (NRI) model: an unsupervised model that learns to infer interactions while simultaneously learning the dynamics purely from observational data. Our model takes the form of a variational auto-encoder, in which the latent code represents the underlying interaction graph and the reconstruction is based on graph neural networks. In experiments on simulated physical systems, we show that our NRI model can accurately recover ground-truth interactions in an unsupervised manner. We further demonstrate that we can find an interpretable structure and predict complex dynamics in real motion capture and sports tracking data. able to reason about the different types of interactions that might arise, e.g. defending a player or setting a screen for a teammate. It might be feasible, though tedious, to manually annotate certain interactions given a task of interest. It is more promising to learn the underlying interactions, perhaps shared across many tasks, in an unsupervised fashion. Recently there has been a considerable amount of work 4687v2 [stat.ML] 6 Jun 2018 Relational inference aims to discover hidden interactions from data and has been studied for decades. Statistical relational learning are based on probabilistic graphical models such as probabilistic relational model (Kemp & Tenenbaum, 2008; Getoor et al., 2001; Koller et al., 2007; Shum et al., 2019) . However, these methods may require significant feature engineering and high computational costs. 1 , NRI simultaneously learns the dynamics from multi-agent trajectories and infers their relations. In particular, NRI builds upon variational auto-encoder (VAE) (Kingma & Welling, 2013) and introduces latent variables to represent the hidden relations. Despite its flexibility, a major limiting factor of NRI is that it assumes the relations among the agents are static. That is, two agents are either interacting or not interacting regardless of their states at different time steps, which is rather restrictive.



Figure1. Physical simulation of 2D particles coupled by invisible springs (left) according to a latent interaction graph (right). In this example, solid lines between two particle nodes denote connections via springs whereas dashed lines denote the absence of a coupling. In general, multiple, directed edge types -each with a different associated relation -are possible.

Figure1: Neural Relational Inference for learning the interaction graph. Picture taken from(Kipf et al., 2018)

