Well, if you look at it deep down, most philosophical systems teach a specific set of core values that is pretty similar across the lot. While the justifications might be different as well as the explanations, but in practice the results are similar. The Stoics, Peripatetics, Epicureans might argue over all kinds of different cosmological points, in terms of ethics the advice on how a person should behave is similar.

That said, many people from the Roman upper class would have had a similar type of education, which would include a philosophical component. Of course not everyone would take it as seriously as someone else, but they would at least know the basic theory. I am sure that all of the so-called Five Good Emperors had been taught philosophy in their youth. Hadrian actually brought back the old Greek philosopher look with the beard, and I think I have read somewhere that he actually attended lectures by Epictetus at Nicopolis. Trajan I believe also had some dealings with philosophers, for example Plutarch. There is the possibility that some of these emperors (Hadrian is a strong candidate) might have kept similar philosophical journals as Marcus, they just didn't survive.