ED/Restrictive EA

Answered

Great question here. First of all, let's start with the traditional differences between ED and REA. ED is binding - if a school accepts you ED, then you must attend. There are very rare instances in which you can get out of an ED acceptance, but this is a difficult process that can result in you being blacklisted from other schools. This is definitely not something you want to do unless there's no other choice. Conversely, REA is non-binding. While you will not be allowed to apply early action or early decision to other private schools, if you are accepted to your REA school, you can still choose to go elsewhere. Typically, applying REA will give you a slight boost in your chancing, while applying ED will give you a massive boost.

Chancing aside, I usually never recommend that students apply ED anywhere if scholarship is an extremely important consideration. First of all, applying ED gives schools no reason to make you a particularly good scholarship offer (after all, they can count on you coming regardless of how much money they offer you). Second, if you are accepted ED you must attend even if you've been given much better scholarship offers elsewhere.

However, the calculation changes slightly because you're looking at the most elite colleges in the country and also because you'll be an international student. At slightly less prestigious programs, merit scholarships are generally an option, and applying ED will often hurt your chances of getting them. The Ivies, though, don't offer merit-based scholarships. Additionally, most US schools don't offer much (if any) scholarship opportunities to international students. However, Harvard and Yale are two of the five schools in the US that are truly need-blind for international students and will meet full demonstrated need for their international students purely with institutional aid. While Columbia is not one of these five schools, US News reports that they offer the largest average scholarship grant to undergraduate international students of any school in the country.

I still think that applying to Columbia ED will involve taking on some risk. Maybe some slightly less selective schools would cut you such generous merit-based scholarships that it would be cheaper to attend them. That said, it may still be worth it to apply ED there because it'll give your chances at an acceptance such a boost, and because you can count on them to at least offer you a reasonable scholarship if you can clearly demonstrate need.

Applying REA to Harvard or to Yale would be a safer option, because it means you'll be able to weigh all your different options at the end of the process. Maybe Boston University offers you a full ride and a stipend and you decide that that's actually a better option for you than attending an Ivy and having to pay for a lot of it. (I had friends who made similar decisions.) REA will give you much less of a boost, though.