Mobileye is doing the learning approach, as described here. I've blogged before about the advantages of this approach. But Alphabet (Google) has spun off its driverless car enterprise into Waymo, which announced this week it would have Chrysler minivans outfitted with its technology on the road by the end of the month. Waymo isn't building its own cars anymore; instead it's providing a package of sensors, computers, and software to be added onto existing cars. As well as I can tell Waymo is still taking the top-down approach, presumably taking advantage of Google Map data and expertise.
The competition between the two approaches will be interesting.