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We study the problem of pursuit-evasion for a single pursuer and an evader in polygonal environments where the players have visibility constraints. The pursuer is tasked with catching the evader as quickly as possible while the evader tries to avoid being captured. We formalize this problem as a zero-sum game where the players have private observations and conflicting objectives.One of the challenging aspects of this game is due to limited visibility. When a player, for example, the pursuer does not see the evader, it needs to reason about all possible locations of the evader. This causes an exponential increase in the size of the state space as compared to the arena size. To overcome the challenges associated with large state spaces, we introduce a new learning-based method that compresses the game state and uses it to plan actions for the players. The results indicate that our method outperforms the existing reinforcement learning methods, and performs competitively against the current state-of-the-art randomized strategy in complex environments.