When n is independent ofδ our approach yields an algorithm whose sample complexityconvergesto 2n2 log 1δ asngrows.

As inthe classical problem, weights are fixed by an adversary and elements appear in random order. In contrast to previous variants of predictions, our algorithm only has access toamuch weakerpiece ofinformation: anadditive gapc.

InstructGPT implements RLHF through several stages, including Supervised Fine-Tuning (SFT), reward model training, and Proximal Policy Optimization (PPO).

This bound naturally breaks into two components.