Ah yes, I didn't want the reader to fuss too much about the idea of a preference, since it's really just an analog of un-normalized pi(modulo the exponentiation part). It doesn't have a strict definition nor is it a formal term. I will un-bold it and italicize it instead. Thank you :)
Hey Joshua, thanks so much for the criticism. I do see your point towards epsilon greedy vs. regret minimization. I will add a section about that before presenting UCB1. I also will add more information in the epsilon-greedy strategy section, elaborating on what the epsilon is really for. I'm not 100% sure how to reframe the nonstationary reward situation, because I feel like that adds state dependent on t to the bandit scenario, which then feels more like MDP.
Thanks for the reply! My audience is for someone who is early into their undergrad degree, doing math or computer science. Which parts do you think is not communicated clearly? I can make an edit later today :)
Great suggestion! The blog was based on a large portion of the book. A friend of mine asked for a version of the first chapter that was digestible for an audience that is in high-school to undergrad college level. I wrote this blog with that in consideration, while adding my own observations as well. I am planning to write up some python solutions for the MDP chapter as well. Thanks for reading :)
Yes, it is as you stated. Due to the fact that bandits are stateless, there is no state parameter in $q_(a,s)$. From where I learned it, this could arguably be an abuse of notation to use $q_$ in the same context. In my newer entry(which is currently WIP), it uses $q_*(a,s)$ and uses cumulative sum of the future rewards(with discount). Thanks for the reply guys :)