Most of the intelligence.org website has been updated very little over the last 4 years, and is thus at least a little out of date. The MIRI reading list in particular hasn't really been updated since before I started at MIRI in 2015.
I can summarize (what I think are the generators of) the MIRI reading list as:
1) If you want to build a philosophically solid reductionist understanding of anything, you should probably start by learning math (theoretical CS is part of math).
2) If you want to work in a preparadigmatic field, focus on breadth and foundations.
3) If the thing you want to understand is about how minds work, things related to epistemics (logic, probability, information theory, topology), optimization (machine learning, game theory, calculus, decision theory), and algorithms maybe should get a little more attention.
(When you also bring in category theory because you want reductionism, which means you need to be consistently viewing the same thing at multiple different levels, this leads to basically the same conclusion as 1+2: learn all fields of math.)
4) Here is our best guess at the best textbook on every subject.
I personally basically haven't read any of those books, so I don't have much to say about point 4, but I believe that Nate learned a bunch of math from many of these exact books.
I stand behind points 1-3, as conditional statements, so if your goal (or your primary instrumental subgoal) is to build a philosophically solid reductionist understanding of how minds work, maybe you should read some of those books.
Note that this advice doesn't have anything to do with MIRI, except in so far as I, and some others at MIRI, are reasonably well described as "trying to build a philosophically solid reductionist understanding of how minds work."
If your plan is to spend 2 years learning all the math, and then reaching out to MIRI saying "I did my homework, can I have a job?" I recommend instead discussing this plan with an actual person at MIRI first.
If on the other hand, it feels obvious to you that you want a philosophically solid reductionist understanding of how minds work, enough that you would still want it if MIRI announced tomorrow that it was pivoting to focus on global poverty, then I recommend you start by learning some math, and I don't have any better advice about what math to learn than what is on that webpage.
I guess I am partially trying to reject the frame of "contributing to all the different research directions that MIRI is pursuing."
Ask not what you can do for agent foundations - ask what agent foundations can do for you, in your own personal quest to figure out how to save the world.
For background on my own research programme, I recommend:
[EDIT: For bandits there's also the textbook "Bandit Algorithms" by Lattimore and Szepesvari, which even has a chapter on reinforcement learning.]
There are some other topics that are important but I'm not sure what reading to recommend: functional analysis [EDIT: maybe "Introductory Functional Analysis with Applications" by Kreyszig], algorithmic information theory, Markov decision processes.
Some books not on the list which I highly recommend:
Question especially for MIRI folks:
The MIRI reading list has not changed very much in several years. But MIRI-associated researchers have been producing what appears to be a significant number of new research directions - for example, Cartesian Frames, Finite Factored Sets, Infra-Bayesianism, and a lot of Stuart Armstrong's research.
Is the research guide up to date and sufficient for contributing to all the different research directions that MIRI is pursuing?