Reward-Aware Population Scaling of Evolutionary Strategies in LLM Fine-Tuning

arXiv:2607.19408v1 Announce Type: new Abstract: Using Evolutionary Strategies (ES) for fine-tuning large language models is attractive because it is memory-efficient, parallel, and compatible with black-box or discrete rewards. Yet its population-size conclusions conflict sharply: fine-tuning with cross-entropy (CE) reward succeeds with $N=1$, while binary-reward training often needs $N \approx 30$. We show this gap is largely about reward design and normalization, not population size. In the capable-model regime we study, z-score advantage normalization can cause $N=2$ to fail. Disabling normalization lets binary-reward ES with $N=2$ improve on GSM8K and TREC across capable models spanning 0.5B-7B, where the normalized variant collapses or degrades. This small-$N$ risk is set by reward granularity: binary accuracy reward induces a zero-advantage probability $q$ that depends in closed form on base accuracy, batch size, and intra-pair correctness correlation; a zero-training probe on Qwen2.5-Instruct/GSM8K matches the formula with mean absolute error 0.020 across 12 configurations and finds the availability threshold $N_{\mathrm{avail}}$ to be small in this capable-model regime. The implication is not that $N=2$ is universally sufficient, but that small-population failure in capable-model binary ES can be an implementation artifact rather than an intrinsic population limit.

Abstract:Using Evolutionary Strategies (ES) for fine-tuning large language models is attractive because it is memory-efficient, parallel, and compatible with black-box or discrete rewards. Yet its population-size conclusions conflict sharply: fine-tuning with cross-entropy (CE) reward succeeds with $N=1$, while binary-reward training often needs $N \approx 30$. We show this gap is largely about reward design and normalization, not population size. In the capable-model regime we study, z-score advantage normalization can cause $N=2$ to fail. Disabling normalization lets binary-reward ES with $N=2$ improve on GSM8K and TREC across capable models spanning 0.5B-7B, where the normalized variant collapses or degrades. This small-$N$ risk is set by reward granularity: binary accuracy reward induces a zero-advantage probability $q$ that depends in closed form on base accuracy, batch size, and intra-pair correctness correlation; a zero-training probe on Qwen2.5-Instruct/GSM8K matches the formula with mean absolute error 0.020 across 12 configurations and finds the availability threshold $N_{\mathrm{avail}}$ to be small in this capable-model regime. The implication is not that $N=2$ is universally sufficient, but that small-population failure in capable-model binary ES can be an implementation artifact rather than an intrinsic population limit.

15 pages, 2 figures. Accepted at the 4th HiLD (High-dimensional Learning Dynamics) Workshop, ICML 2026

Machine Learning (cs.LG)

arXiv:2607.19408 [cs.LG]

(or arXiv:2607.19408v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.19408 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Reward-Aware Population Scaling of Evolutionary Strategies in LLM Fine-Tuning

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