You may notice that among the early emperors there are few beards. Beards were often associated with philosophers.
"Come, let us leave the chief works of nature, and behold what she works by the way. Is anything more useless than the hairs upon the chin? Did she not use even these in the most suitable way she could? Did she not by these means distinguish male and female? Does not the nature of each one of us cry aloud from afar, 'I am a man: on these terms approach me and address me; seek nothing else. Behold the signs.' Again, in women nature took the hair from their face, even as she mingled in their voice a softer note. What! You say the creature ought to have been left undistinguished and each of us to have proclaimed, 'I am a man'? Nay, but how noble and comely and dignified is this sign, how much more fair than the cock's crest, how much more magnificent than the lion's mane! Therefore we ought to preserve the signs God has given; we ought not to abandon them, nor, so far as in us lies, to confound the sexes which have been distinguished."The Augustan History, which contains biographies of the emperors from Hadrian to Elagabalus, says Hadrian wore a beard because of facial blemishes.
Epictetus I.XVI: OnProvidence