Compute Allocation for Self-Evolving LLMs: 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 when measured in 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.

Computation and Language (cs.CL); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Neural and Evolutionary Computing (cs.NE)

arXiv:2605.29268 [cs.CL]

(or arXiv:2605.29268v3 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2605.29268 Focus to learn more arXiv-issued DOI via DataCite

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