I agree that the proof here can be made significantly more general—and I agree that exploring that definitely seems worthwhile—though I also think it’s worth pointing out that the proof rests on assumptions that I would be a lot less confident would hold in other situations. The point of explaining the detail regarding search algorithms here is that it gives a plausible story for why the assumptions made regarding πlearn and Tbad should actually hold.
I agree that the proof here can be made significantly more general—and I agree that exploring that definitely seems worthwhile—though I also think it’s worth pointing out that the proof rests on assumptions that I would be a lot less confident would hold in other situations. The point of explaining the detail regarding search algorithms here is that it gives a plausible story for why the assumptions made regarding πlearn and Tbad should actually hold.