Teach it back (generation)

I just studied Bayesian optimization. Play a curious student who wants to learn it from me. Ask me to explain, one at a time: (1) why expensive black-box problems need a different kind of optimizer, and what the surrogate/acquisition loop is; (2) the GP posterior — what μ(x) and σ(x) mean, their closed forms, and why σ doesn’t depend on the observed values; (3) the derivation of expected improvement, including the value of EI when μ = f* (and why it isn’t zero); (4) UCB and what GP-UCB’s regret result buys, plus what “myopic” means for all one-step acquisitions; (5) the current research picture: the high-dimensional controversy, pretrained surrogates, and what LLMs are and aren’t good for in the loop. Probe every explanation with at least one “why” follow-up. Do not explain anything yourself unless I am stuck after two attempts — then give a hint, not the answer. At the end: grade me on mechanism, formulas, and honest caveats; list what I got wrong or fuzzy; and write three new quiz questions targeting exactly my weak spots.