  We consider surveillance-evasion differential games, where a pursuer must try
to constantly maintain visibility of a moving evader. The pursuer loses as soon
as the evader becomes occluded. Optimal controls for game can be formulated as
a Hamilton-Jacobi-Isaac equation. We use an upwind scheme to compute the
feedback value function, corresponding to the end-game time of the differential
game. Although the value function enables optimal controls, it is prohibitively
expensive to compute, even for a single pursuer and single evader on a small
grid. We consider a discrete variant of the surveillance-game. We propose two
locally optimal strategies based on the static value function for the
surveillance-evasion game with multiple pursuers and evaders. We show that
Monte Carlo tree search and self-play reinforcement learning can train a deep
neural network to generate reasonable strategies for on-line game play. Given
enough computational resources and offline training time, the proposed model
can continue to improve its policies and efficiently scale to higher
resolutions.
