Yes, your explanations are clear and are also how I understood the paper, but I feel like there's some motivation for the RL training that's missing. Why not "pseudo labeling"? Why is the RL approach better? Also the reward score is non-differentiable because it was designed that way, but they could have designed it to be differentiable. For example instead of decoding the log probs why not train the reward model on them directly? You can still obtain the labels via decoding them doesn't mean that has to be the input to the reward model. There are a number of design choice the authors made that are not motivated in the paper. I haven't read the reference so maybe they are motivated elsewhere in the literature, but RL seems like a strange choice for this problem since there isn't a dynamic environment that the agent is interacting with.