Problem: Discovering good problem-solving strategies, called heuristics, for hard optimization problems often requires many calls to Large Language Models (LLMs). Using the most powerful model each time is expensive, and it turns out that cheaper models sometimes do better.
What was done: Researchers developed Ballad, an algorithm that learns to pick which LLM to call next based on results seen so far. It tracks which models have produced rare, excellent heuristics and adapts as the search evolves.
Main finding: On several hard problems, Ballad matched or beat the best single model and reduced cost by up to 65.6%. This shows that adaptively combining multiple models can be both more effective and cheaper than relying on one frontier model.