I like this avatar; it's clean and really draws your attention.
I was thinking of ways to improve it - not that there is anything wrong with it! I've started trying my hand at more in-depth C&C for my own learning, too. I really hope this doesn't come across as annoying or pedantic. Anyway, here is some C&C if you are interested!
The banding on the grey line on the glasses is very chunky looking. You could try abstracting the grey bits away from the glasses. That would open up a colour slot that you could use for a pink colour to make some AA on the white line. The same pink could be used on the part of the glasses where the background is visible through them to give a transparent effect. Other suggestions could be using the skin tones to do some light AA on the hair, and also the shades of purple on the shirt are very close so some more contrast could show off your shading. In fact, you could darken the shadow of the shirt and use that colour for the glasses, freeing up another colour slot to do AA on the shirts shadow. Also, I spotted two minor jaggies on his (your) shoulder.
I drew up these changes so you can have a look, here. It might not be to your taste but if there is anything here you can use, please do, and if you hate it, feel free to ignore it! 
And please don't hesitate to strictly C&C anything I upload, too!
Wow, thank you so much for these practical advice. Your option is much better than mine.