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Designing effective heuristics for diverse combinatorial optimization problems requires substantial expertise and repeated search. Large language models (LLMs) automate heuristic generation and refinement, but heuristic search typically depends on evaluation feedback from the problem being optimized. Generalizing to ne...
Zeroth-order (ZO) optimization offers a memory-efficient alternative for LLM fine-tuning by estimating updates only from forward evaluations of perturbed parameters, without backpropagation or activation storage. However, in billion-parameter LLMs, isotropic perturbations often waste many forward evaluations on weakly...
This work proposes Hyper-ES, a subspace-based ES framework that avoids the weakness of ES in full-parameter search while exploiting its strength in low-dimensional optimization, and consistently outperforms GRPO-LoRA while requiring 10% fewer space-consuming gradient updates.
These findings position ES as a distinct reasoning post-training paradigm rather than a less effective, memory-efficient alternative to GRPO, and study how hyperparameter design affects the effectiveness of ES, demonstrating that ES requires a smaller population size in a larger LLM.
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