I had this problem with my weekly paper being stolen on Mondays and Thursdays (why? I'm not sure).
I sat up and waited and waited (paper gets delivered around 0400 am) for the perp. I went into the old LRRP mode.
It was a neighbor from the next block who drives past the house to get to the highway (and, incidently, to check the mail - we have community mailboxes, aka rural route post next to my house).
It was a WOMAN!
No problem, I waited until the next time she was to shop my driveway (she showed consistenly before going to work around 0615 - 0630). I left her a surprise (I elected to be playful instead of vindictive). I started to put old papers out in place of the current editions.
I thought that was pretty funny - and it got her to stop.
My initial reaction was to leave a Monday paper next to her four flat tires - but I knew she'd know it was me and could potentially start a local war. So, problem solved, no conflict in the neighborhood, and someone's house to target with eggs on Holloween.
Hope this gives you an idea.