  Pursuit-evasion games (PEGs) model interactions between a team of pursuers
and an evader in graph-based environments such as urban street networks. Recent
advancements have demonstrated the effectiveness of the pre-training and
fine-tuning paradigm in PSRO to improve scalability in solving large-scale
PEGs. However, these methods primarily focus on specific PEGs with fixed
initial conditions that may vary substantially in real-world scenarios, which
significantly hinders the applicability of the traditional methods. To address
this issue, we introduce Grasper, a GeneRAlist purSuer for Pursuit-Evasion
pRoblems, capable of efficiently generating pursuer policies tailored to
specific PEGs. Our contributions are threefold: First, we present a novel
architecture that offers high-quality solutions for diverse PEGs, comprising
critical components such as (i) a graph neural network (GNN) to encode PEGs
into hidden vectors, and (ii) a hypernetwork to generate pursuer policies based
on these hidden vectors. As a second contribution, we develop an efficient
three-stage training method involving (i) a pre-pretraining stage for learning
robust PEG representations through self-supervised graph learning techniques
like GraphMAE, (ii) a pre-training stage utilizing heuristic-guided multi-task
pre-training (HMP) where heuristic-derived reference policies (e.g., through
Dijkstra's algorithm) regularize pursuer policies, and (iii) a fine-tuning
stage that employs PSRO to generate pursuer policies on designated PEGs.
Finally, we perform extensive experiments on synthetic and real-world maps,
showcasing Grasper's significant superiority over baselines in terms of
solution quality and generalizability. We demonstrate that Grasper provides a
versatile approach for solving pursuit-evasion problems across a broad range of
scenarios, enabling practical deployment in real-world situations.
