In this work we propose a reinforcement learning (RL) framework that controls the density of a large-scale swarm for engaging with adversarial swarm attacks. Although there is a significant amount of existing work in applying artificial intelligence methods to swarm control, analysis of interactions between two adversarial swarms is a rather understudied area. Most of the existing work in this subject develop strategies by making hard assumptions regarding the strategy and dynamics of the adversarial swarm. Our main contribution is the formulation of the swarm to swarm engagement problem as a Markov Decision Process and development of RL algorithms that can compute engagement strategies without the knowledge of strategy/dynamics of the adversarial swarm. Simulation results show that the developed framework can handle a wide array of large-scale engagement scenarios in an efficient manner.