[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.
For background on my own research programme, I recommend:
“Computational Complexity” by Goldreich
“Probability: Theory and Examples” by Durrett
“Understanding Machine Learning” by Shalev-Shwartz and Ben-David
“Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems” by Bubeck and Cesa-Bianchi
[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.
Thanks!