The basic loop is: (i) generate synthetic data, (ii) rate synthetic data, (iii) update model to put more probability on better data and less probability on worse data, then go back to (i).
As far as I know it doesn't work very well so far. It is prone to overfitting, where it ranks highly some trivial detail of the output eg "if a summary starts with a byline of the author its a sign of quality" and then starts looping on itself over and over, increasing the frequency and size of bylines until it's totally crommed off to infinity and just repeating a short phrase endlessly. Humans have good baselines and common sense that these ML systems lack, if you've ever seen one of those "deep dream" images it's the same kind of idea. The "most possible dog" image can be looks almost nothing like a dog in the same way that the "most possible poem" may look nothing like a poem.
> This technique, the "Self-Taught Reasoner" (STaR), relies on a simple loop: generate rationales to answer many questions, prompted with a few rationale examples; if the generated answers are wrong, try again to generate a rationale given the correct answer; fine-tune on all the rationales that ultimately yielded correct answers; repeat. We show that STaR significantly improves performance on multiple datasets compared to a model fine-tuned to directly predict final answers
But there are a few others. In general good data is good data. We're definitely learning more about how to produce good synthetic version.
Data smuggling is a known phenomenon in similar tasks.
If the model generates data of variable quality, and if there's a good way to distinguish good data from bad data, then training on self-generated data might "bootstrap" a model to better performance.
This is common in reinforcement learning. Famously, AlphaGo Zero (https://en.wikipedia.org/wiki/AlphaGo_Zero) learned exclusively on self-play, without reference to human-played games.
Of course, games have a built-in critic: the better strategy usually wins. It's much harder to judge the answer to a math problem, or decide which essay is more persuasive, or evaluate restaurant recommendations.