Probabilistic Symmetry for Multi-Agent Dynamics

TL;DR

This paper introduces PECCO, a novel probabilistic model leveraging symmetry in multi-agent dynamics to improve prediction accuracy and uncertainty calibration, with demonstrated success on synthetic and real datasets.

Contribution

The paper presents PECCO, a new deep equivariant convolution model that incorporates symmetry for probabilistic multi-agent trajectory prediction, enhancing accuracy and uncertainty calibration.

Findings

PECCO outperforms non-equivariant baselines in accuracy.

PECCO achieves better uncertainty calibration.

The model effectively captures joint velocity distributions.

Abstract

Learning multi-agent dynamics is a core AI problem with broad applications in robotics and autonomous driving. While most existing works focus on deterministic prediction, producing probabilistic forecasts to quantify uncertainty and assess risks is critical for downstream decision-making tasks such as motion planning and collision avoidance. Multi-agent dynamics often contains internal symmetry. By leveraging symmetry, specifically rotation equivariance, we can improve not only the prediction accuracy but also uncertainty calibration. We introduce Energy Score, a proper scoring rule, to evaluate probabilistic predictions. We propose a novel deep dynamics model, Probabilistic Equivariant Continuous COnvolution (PECCO) for probabilistic prediction of multi-agent trajectories. PECCO extends equivariant continuous convolution to model the joint velocity distribution of multiple agents. It uses dynamics integration to propagate the uncertainty from velocity to position. On both synthetic and real-world datasets, PECCO shows significant improvements in accuracy and calibration compared to non-equivariant baselines.