As a doctoral student, you take some classes, but most of what you do needs material that you must gather from papers, conferences, and other sources. With limited possibilities for communication with authors and such, what's the best way to learn these necessary concepts?
For example, I read a paper (from a big name publication) presenting a novel approach to SVMs with new constraints on the objective function. The description of the optimization was vague, but I needed to use this technique for my own work and my optimization skills are limited at best. I'm sure to a reviewer with the right expertise, the description was fine though.
As a PhD student, one can only take so many courses in so many subjects. Nevertheless, some things (like optimization theory in the above example) are not exactly easily self-taught, and surely not in a few weeks.
So I ask you, what is the best strategy to fill these gaps without devoting entire courses to the subject?
Additionally, how do you do that without just learning things piecemeal? Learning something useful for a hyper-specific case is essentially worthless once circumstances change. How do you balance the need to know both these hyper-specific examples and the more general ideas while doing this gap-filling?