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

arXiv: https://arxiv.org/abs/2603.15907 · HTML: https://mlsanity.com/paper/2603.15907/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Adversarial robustness and RL in finance, one of 15 directions in Deep reinforcement learning methods.
- Builds on 14 of its 24 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Placed in

- Deep reinforcement learning methods / [Adversarial robustness and RL in finance](https://mlsanity.com/deeprl/adversarial-robustness-and-rl-in-finance/)

## Builds on (most cited first, 14 of 14)

- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [The Surprising Effectiveness of PPO in Cooperative, Multi-Agent Games](https://mlsanity.com/paper/2103.01955/) (2021)
- [VMAS: A Vectorized Multi-Agent Simulator for Collective Robot Learning](https://mlsanity.com/paper/2207.03530/) (2022)
- [BenchMARL: Benchmarking Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2312.01472/) (2023)
- [An Introduction to Pursuit-evasion Differential Games](https://mlsanity.com/paper/2003.05013/) (2020)
- [Cooperative Team Strategies for Multi-player Perimeter-Defense Games](https://mlsanity.com/paper/1912.04342/) (2019)
- [Multiple Pursuer Multiple Evader Differential Games](https://mlsanity.com/paper/1911.03806/) (2019)
- [Competitive Perimeter Defense of Conical Environments](https://mlsanity.com/paper/2110.04667/) (2021)
- [Task Assignment for Multiplayer Reach-Avoid Games in Convex Domains via Analytical Barriers](https://mlsanity.com/paper/1904.02789/) (2019)
- [Perimeter-defense Game on Arbitrary Convex Shapes](https://mlsanity.com/paper/1909.03989/) (2019)
- [One Apollonius Circle is Enough for Many Pursuit-Evasion Games](https://mlsanity.com/paper/2111.09205/) (2021)
- [Guarding a Target Area from a Heterogeneous Group of Cooperative Attackers](https://mlsanity.com/paper/2407.00762/) (2024)
- [Heterogeneous Roles against Assignment Based Policies in Two vs Two Target Defense Game](https://mlsanity.com/paper/2409.09302/) (2024)
- [Cooperative Target Defense under Communication and Sensing Constraints](https://mlsanity.com/paper/2412.09939/) (2024)

## Abstract (arXiv)

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.