Have you considered writing a bot as a mod for a game, instead of from a kit like Unity/UDK?
e.g. if you mod an Unreal Engine game that has a modding SDK, then it will likely similar to the UDK (seeing the UDK is just a free Unreal Engine), but with a FPS game's assets and game rules ready to go.

Have you considered writing a bot as a mod for a game, instead of from a kit like Unity/UDK. e.g. if you mod an Unreal Engine game, then it's likely got a modding SDK similar to the UDK, but with FPS assets and game rules ready to go.