# Understanding Evolution Strategies for LLM Reasoning: Broader Reasoning Coverage than GRPO

arXiv: https://arxiv.org/abs/2608.27351 · HTML: https://mlsanity.com/paper/2608.27351/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 34 of its 45 references that are in the map.
- First posted on arXiv 27 Aug 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 34)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining](https://mlsanity.com/paper/2504.07912/) (2025)
- [Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmark](https://mlsanity.com/paper/2402.11592/) (2024)
- [JustRL: Scaling a 1.5B LLM with a Simple RL Recipe](https://mlsanity.com/paper/2512.16649/) (2025)
- [Variance-reduced Zeroth-Order Methods for Fine-Tuning Language Models](https://mlsanity.com/paper/2404.08080/) (2024)
- [Evolution Strategies at Scale: LLM Fine-Tuning Beyond Reinforcement Learning](https://mlsanity.com/paper/2509.24372/) (2025)
- [RL Fine-Tuning Heals OOD Forgetting in SFT](https://mlsanity.com/paper/2509.12235/) (2025)
- [Neural Thickets: Diverse Task Experts Are Dense Around Pretrained Weights](https://mlsanity.com/paper/2603.12228/) (2026)
- [Evolution Strategies at the Hyperscale](https://mlsanity.com/paper/2511.16652/) (2025)
- [Revisiting Entropy in Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2511.05993/) (2025)
- [SofT-GRPO: Surpassing Discrete-Token LLM Reinforcement Learning via Gumbel-Reparameterized Soft-Thinking Policy Optimization](https://mlsanity.com/paper/2511.06411/) (2025)
- [Mitigating Forgetting Between Supervised and Reinforcement Learning Yields Stronger Reasoners](https://mlsanity.com/paper/2510.04454/) (2025)
- [Entropy-Preserving Reinforcement Learning](https://mlsanity.com/paper/2603.11682/) (2026)
- [Matching Accuracy, Different Geometry: Evolution Strategies vs GRPO in LLM Post-Training](https://mlsanity.com/paper/2604.01499/) (2026)
- [Reasoning-CV: Fine-tuning Powerful Reasoning LLMs for Knowledge-Assisted Claim Verification](https://mlsanity.com/paper/2505.12348/) (2025)
- [ESSA: Evolutionary Strategies for Scalable Alignment](https://mlsanity.com/paper/2507.04453/) (2025)

## Built on by (most cited first, 1 of 1)

- [AIM-ZO: Activation-Informed Subspace Maintenance for Zeroth-Order LLM Fine-Tuning](https://mlsanity.com/paper/2609.35257/) (2026)

## Abstract (arXiv)

Evolution Strategies (ES) have recently emerged as a memory-efficient post-training paradigm for LLM reasoning. However, the optimization behavior of ES remains understudied, making it hard to define its advantage scope compared to mainstream post-training paradigms (e.g., Group Relative Policy Optimization (GRPO)). By systematically investigating ES dynamics and mechanisms, this paper first identifies a performance advantage of ES over GRPO, theoretically and empirically showing that ES can lead to broader reasoning coverage, thereby better exploiting the reasoning capabilities of pretrained LLMs. Theoretically, we show that verifier-projected Jensen-Shannon diversity across the ES population is helpful to higher Pass@K performances. Empirically, unlike GRPO, which exhibits entropy collapse, ES improves Pass@1 while attaining higher Pass@K than GRPO. We further develop a sequential GRPO-ES training strategy that combines GRPO's strength in Pass@1 with ES's gains in Pass@K. Second, we find that despite substantial whole-model parameter drift, the task-performance gains of ES are only contributed to a sparse subset of larger-magnitude updates. This functional sparsity suggests that large parameter movement need not imply widespread functional change, and held-out evaluations further show that it does not necessarily lead to catastrophic forgetting. Finally, we study how hyperparameter design affects the effectiveness of ES, demonstrating that ES requires a smaller population size in a larger LLM. These findings position ES as a distinct reasoning post-training paradigm rather than a less effective, memory-efficient alternative to GRPO.