Fast and the Furious: Hot Starts in Pursuit-Evasion Games

TL;DR

This work addresses the challenge of placing pursuers when evader locations are unknown by offline generating heat-start configurations through a Pareto-front Graph Feature Space and a Graph Convolutional Network trained on Pareto-optimal graphs. It combines multi-objective optimization (via NSGA-II), graph-structured learning, and differential-game-inspired controls across continuous spaces, demonstrated in many-evaders and many-pursuers scenarios using MPE. The key contributions include defining a three-objective graph feature set, constructing a graph space with PP and PE edges, training a GCN to produce effective hot starts, and empirically showing statistically significant improvements in evader survival and pursuer containment. The approach offers a scalable, knowledge-accumulating method that can enhance real-world pursuit-evasion applications where upfront strategic initialization is essential.

Abstract

Effectively positioning pursuers in pursuit-evasion games without prior knowledge of evader locations remains a significant challenge. A novel approach that combines game-theoretic control theory with Graph Neural Networks is introduced in this work. By conceptualizing pursuer configurations as strategic arrangements and representing them as graphs, a Graph Characteristic Space is constructed via multi-objective optimization to identify Pareto-optimal configurations. A Graph Convolutional Network (GCN) is trained on these Pareto-optimal graphs to generate strategically effective initial configurations, termed "hot starts". Empirical evaluations demonstrate that the GCN-generated hot starts provide a significant advantage over random configurations. In scenarios considering multiple pursuers and evaders, this method hastens the decline in evader survival rates, reduces pursuer travel distances, and enhances containment, showcasing clear strategic benefits.

Figures (6)

• Figure 1: Images of a hot start and a random start in 4 Pursuer vs. 2 Evader Game (pursuers are in red and evaders are in green).
• Figure 2: Image of 5 pursuers (in red) surrounding an evader (in green), illustrating cooperative containment. Black circles represent capture radii.
• Figure 3: Pipeline diagram of the Pursuit-Evasion Games framework. Starting from the MPE Simple Tag Environment, the process follows these steps: 1. Generate data using control algorithms; 2. Construct the Graph Feature Space (GFS) and identify Pareto frontiers; 3. Train the Graph Convolutional Network (GCN); 4. Generate Hot Starts (each red dot represents x and y coordinates); 5. Apply these Hot Starts to the control algorithm; and 6. Perform statistical evaluation.
• Figure 4: Example Heat Maps for Many Pursuers vs. Many Evaders Games. The brighter the color, the more activity in that area of movement. See Appendix section G.4 for heatmaps for all Many Pursuers vs. Many Evaders Games.
• Figure 5: Survival Analysis for Many Pursuers vs. Many Evaders Game Simulations. The x-axis is the time step and the y-axis is the value of the Kaplan-Meier Estimator.