Zheng, Wu, Zhang and colleagues posted Dream-RSI. The slogan is recursive self-improvement. The method is simpler.
They do not retrain the model. They do not replace the coding agent. They rewrite only the search rule: where to continue, how many branches to open at once, and when to stop.
A finished job is already a tree. Each node is one attempt, with the score it got and what it cost. A new search rule does not have to run those attempts again. It walks the same tree in a different order. If it asks for a branch that was never tried, that walk gets no credit. The tree is not a guess about the future. It is a record of what already happened.
That walk is the whole trick. Rank the new rule on work you already paid for. Keep the old rule in the contest so you do not ship something that looks worse on the same record. Then, if the new rule wins, spend a fresh round. The fresh round is required. The tree cannot invent attempts you never ran. Without that round you are only sorting old luck.
Their clean comparison keeps the same agent and the same starting rule, and never changes the rule after round one. Dream-RSI does change it after walking the tree. On a Lasso solver task they report fewer agent calls and a better average runtime on held-out data. The average hides mixed results on single datasets. Comparisons to other labs on other models and much larger budgets are not the same test. Putting old lessons into the prompt did worse than walking the tree.
What you can take
This helps when an agent already retries: coding, search, drafting, anything with a score you can read without a person in the loop.
Keep each attempt. Parent, child, score, cost. That is the tree.
Before you buy another round, try the next search rule on that tree. Would it have opened this branch. Would it have stopped here. Would it have run these together. If it wants a move you never made, give it no credit from the old tree.
If the walk is not better than what you already did, do not spend the round. If it is better, spend one live round and add those new attempts to the tree. Then stop or repeat.
It fails when you have no score, when the tree is a handful of tries, or when the next job is a different shape from the last one. Then you are just searching again, which is the normal cost.
A log, a walk, one paid round when the walk earns it.