Compute Allocation in Evolutionary Search: From Depth-Breadth to Multi-Armed Bandits
Abstract
LLM-guided evolutionary search (Evolve systems) has reached state-of-the-art results on mathematical and combinatorial tasks, yet most existing systems report only the best of many runs and leave the run-to-run distribution undocumented. We ask how a fixed budget of LLM calls should be allocated, and how reliably a single run reaches the reported numbers. Sweeping the depth-breadth grid over five models and three tasks, we identify two empirical regularities: a fitness-compute envelope along which capability ordering largely collapses on effective FLOPs, and a bilinear depth-breadth fit with task-specific interaction; both are gated by model-task capability. Motivated by these regularities, we propose BaSE (Bandit-based Self-Evolving), a multi-armed bandit that allocates LLM calls across parallel trajectories. Without changing the model, prompt, or evaluator, BaSE improves mean fitness by 12.3% over the strongest island-protocol baseline across 8 (model, task) cells, with the largest gains on high-variance settings: a reliability gain from allocation alone.
Cite
@article{arxiv.2605.29268,
title = {Compute Allocation in Evolutionary Search: From Depth-Breadth to Multi-Armed Bandits},
author = {Sixue Xing and Haoyu He and Kerui Wu and Zhuo Yang and Haozheng Luo and Tianfan Fu and Aarthy Nagarajan},
journal= {arXiv preprint arXiv:2605.29268},
year = {2026}
}