Game-Theory-Assisted Reinforcement Learning for Border Defense: Early Termination based on Analytical Solutions

2026-03-16

AI Summary

针对边境防御中感知受限问题，结合博弈论与强化学习，利用阿波罗尼奥斯圆实现早期终止，提升搜索策略学习效率。

Technology Category

• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Security and privacy of machine learning and AI applications

Abstract

Game theory provides the gold standard for analyzing adversarial engagements, offering strong optimality guarantees. However, these guarantees often become brittle when assumptions such as perfect information are violated. Reinforcement learning (RL), by contrast, is adaptive but can be sample-inefficient in large, complex domains. This paper introduces a hybrid approach that leverages game-theoretic insights to improve RL training efficiency. We study a border defense game with limited perceptual range, where defender performance depends on both search and pursuit strategies, making classical differential game solutions inapplicable. Our method employs the Apollonius Circle (AC) to compute equilibrium in the post-detection phase, enabling early termination of RL episodes without learning pursuit dynamics. This allows RL to concentrate on learning search strategies while guaranteeing optimal continuation after detection. Across single- and multi-defender settings, this early termination method yields 10-20% higher rewards, faster convergence, and more efficient search trajectories. Extensive experiments validate these findings and demonstrate the overall effectiveness of our approach.

Problem

• border defense
• limited perceptual range
• reinforcement learning
• game theory
• differential games

Innovation

• Game Theory
• Reinforcement Learning
• Early Termination
• Apollonius Circle
• Border Defense