Most implementations I'm seeing for playing games like Atari (usually similar to DeepMind's work using DQN) have 4 graphical frames of input fed into 3 convolutional layers which are then fed into a single fully connected layer. The explanation of no pooling layer is due to positioning of features/objects being very critical to most games.
My concern with this is that it may be weighing visual features based on position without regard for feature->feature proximity. By this, I mean to question if learning to avoid bullets in the bottom left of the screen is knowledge also used in the bottom right of the screen in a game like Space Invaders.
So, question 1: Is my concern with only using 3 conv layers into a fc layer legitimate regarding spatially localized learning?
Question 2: If my concern is legitimate, how might the network be modified to still treat feature position as significant, but to also take note of feature to feature proximity?
(I'm still quite the novice if that isn't extremely obvious, so if my questions aren't completely ridiculous on their own, please try to keep responses relatively high level if you would.)