What? America doesn't believe in R&D much?

I'd push back rather hard on that statement. US companies invest loads of cash in R&D, more than any other country. The problem is that if you expect to be doing R&D for a YC startup (or even a typical SV consumer web or B2B startup), you're really barking up the wrong tree—those sorts of companies don't do a lot of R&D. If you're really interested in that kind of work, you'd be far better off in bioscience or hardware. Or at least larger, established software companies.

You need to be careful on how you define R&D. Pure R&D, the kind of culture that spawned say UNIX, Oak (Java) or Plan 9 etc is on the decline as in recent years the bean counters tend to look at pure R&D as a waste of money as there is no medium term return on investment. Look at the decline of IBM Research in the US as an example. Google and in some cases Microsoft are exceptions to this.

However the US tax code allows companies to write off new development of new systems as a tax break, so you typically would be doing this kind of R&D at a startup until the system moves into production and is then accounted for differently for tax purposes.

So US companies invest load of cash in R&D, just not the traditional kind of Pure R&D.

Yeah, this is what I was referring to. Pike lamented this in his famous essay, "Systems Software Research is Dead." In it's place, we tend to have more focused R&D, which is still kind of nifty, but can imply a certain amount of acquiescence with the status quo.

In software, Microsoft Research, IBM Research, Intel OTC, Qualcomm QuIC, etc. come to mind.

I have no idea. Google X, Facebook AI Lab? I'm struggling with this myself, the solutions (for me) now seem to be: learn something new every year at work (by changing the technologies your employer uses or changing employers), and research in the afternoon.

I did exactly this - did my research after work, when my employer didn't budge in terms of putting on new technologies, or even improving it, I changed.

The other move is to do a start-up and work on one's own R&D (how you do it is your call)

The problem is that I'm interested in robotics/AI, which (right now) seems to be a high-investment/low-probability-of-success endeavor.

On the contrary. I feel like if you can prove competency at depth in AI/robotics, you will be absolutely _set_ for the next ~half century of computing. The sort of problems we're solving in the areas of machine learning/planning have applicability literally everywhere, even outside of STEM fields. (looking at you, social sciences, a big data / machine learning twist is certainly in your future)

The hard part is the "proving competency" part. I consider myself a somewhat competent programmer, but trying to catch myself up on the state of the art in my focus; N body simulation; is a hard enough problem, and even when you feel like you understand it, how do you let other people know? (little bit of chicken in egg here, since normally the PHD is this sort of signalling.)

The answer I chose is "build fun projects in my free time." and with the advent of more accessible programmable robotics, you can certainly explore both of your interests. (I should take my own advice here too...)