How is it possible for perturbation-based methods like Evolution Strategies (ES) to optimize billion-parameter large language models (LLMs)? Classical search methods are highly dependent on finding good candidates within generated populations. However, when using ES to fine-tune LLMs, a phenomenon can occur where all offspring models consistently perform worse than the parent model, yet during training, the parent model consistently improves. This paradox occurs across models, tasks, and even modalities. This paper characterizes the paradox, then examines how the local reward landscape and properties of the ES estimator contribute to it: in high-dimensional spaces, exploration leads to worse performance, yet still highlights good directions; aggregating those directions then allows for making local improvements. The result can be seen as a new optimization paradigm where a principled interaction of noise and curvature produces the paradox as a byproduct of effective optimization. These findings provide guidance for taking advantage of perturbation-based methods in LLM fine-tuning and in high-dimensional optimization in general.

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