# Evolution Strategies at Scale: LLM Fine-Tuning Beyond Reinforcement Learning

arXiv: https://arxiv.org/abs/2509.24372 · HTML: https://mlsanity.com/paper/2509.24372/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 90 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 30 of 60)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [BloombergGPT: A Large Language Model for Finance](https://mlsanity.com/paper/2303.17564/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Towards Expert-Level Medical Question Answering with Large Language Models](https://mlsanity.com/paper/2305.09617/) (2023)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)

## Built on by (most cited first, 30 of 34)

- [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)
- [The Blessing of Dimensionality in LLM Fine-tuning: A Variance-Curvature Perspective](https://mlsanity.com/paper/2602.00170/) (2026)
- [Matching Accuracy, Different Geometry: Evolution Strategies vs GRPO in LLM Post-Training](https://mlsanity.com/paper/2604.01499/) (2026)
- [Evolutionary Strategies lead to Catastrophic Forgetting in LLMs](https://mlsanity.com/paper/2601.20861/) (2026)
- [Quantized Evolution Strategies: High-precision Fine-tuning of Quantized LLMs at Low-precision Cost](https://mlsanity.com/paper/2602.03120/) (2026)
- [EA4LLM: A Gradient-Free Approach to Large Language Model Optimization via Evolutionary Algorithms](https://mlsanity.com/paper/2510.10603/) (2025)
- [Distributional Biases in Post-Training: A Markovian Analysis of Reasoning Trajectories](https://mlsanity.com/paper/2511.07368/) (2025)
- [Hard Constraints Meet Soft Generation: Guaranteed Feasibility for LLM-based Combinatorial Optimization](https://mlsanity.com/paper/2602.01090/) (2026)
- [Overcoming Forgetting in LLM Fine-Tuning with Evolution Strategies](https://mlsanity.com/paper/2605.30148/) (2026)
- [Mistake Notebook Learning: Batch-Clustered Failures for Training-Free Agent Adaptation](https://mlsanity.com/paper/2512.11485/) (2025)
- [Fine-Tuning Language Models to Know What They Know](https://mlsanity.com/paper/2602.02605/) (2026)
- [PopuLoRA: Co-Evolving LLM Populations for Reasoning Self-Play](https://mlsanity.com/paper/2605.16727/) (2026)
- [Beyond the Best Guess: Improving LLM Solution Coverage with Evolution Strategies](https://mlsanity.com/paper/2608.12679/) (2026)
- [Training Non-Differentiable Networks via Optimal Transport](https://mlsanity.com/paper/2605.01928/) (2026)
- [Decomposing Evolutionary Mixture-of-LoRA Architectures: The Routing Lever, the Lifecycle Penalty, and a Substrate-Conditional Boundary](https://mlsanity.com/paper/2605.11153/) (2026)
- [Hyper-ES: Effective Evolution Strategies for LLM Reasoning via Descent Direction Merging](https://mlsanity.com/paper/2608.05541/) (2026)
- [Understanding Evolution Strategies for LLM Reasoning: Broader Reasoning Coverage than GRPO](https://mlsanity.com/paper/2608.27351/) (2026)
- [Coverage, Not Credit: Failure-Credit Routing of Zeroth-Order Perturbation Budgets Does Not Improve On-Pool Sample Efficiency for LLM Agents](https://mlsanity.com/paper/2608.28011/) (2026)
- [TerMeZO: Ternary Sparse Zeroth-Order Optimization for Fine-tuning BitNet Models at the Edge](https://mlsanity.com/paper/2609.33548/) (2026)
- [Optimize Wider, Not Deeper: Consensus Aggregation for Policy Optimization](https://mlsanity.com/paper/2603.12596/) (2026)
- [Goal-Conditioned Supervised Learning for LLM Fine-Tuning](https://mlsanity.com/paper/2605.16345/) (2026)
- [Inference-Native Zeroth-Order Optimization for LLMs](https://mlsanity.com/paper/2605.28760/) (2026)
- [Genetic Algorithms with Optimization Guided Operators](https://mlsanity.com/paper/2606.12279/) (2026)
- [Reward-Aware Population Scaling of Evolutionary Strategies in LLM Fine-Tuning](https://mlsanity.com/paper/2607.19408/) (2026)
- [Can Bayesian Optimization Efficiently Find a Strong Single Expert in Neural Thickets?](https://mlsanity.com/paper/2608.10867/) (2026)
- [Hill Sampling for Test-Time Scaling: A Simple and Better Alternative to Repeated Sampling, Evolution, and Training](https://mlsanity.com/paper/2609.25510/) (2026)
- [Modular Norm RandOpt: Population-Efficient Ensembling through Architecture-Aware Perturbations](https://mlsanity.com/paper/2609.25745/) (2026)
- [Traversing the solution space of neural networks with Hessian Null Space Continuation](https://mlsanity.com/paper/2609.38081/) (2026)
- [Continual Reinforcement Learning with Neuroevolution](https://mlsanity.com/paper/2610.01583/) (2026)

## Abstract (arXiv)

Fine-tuning large language models (LLMs) for downstream tasks is an essential stage of modern AI deployment. Reinforcement learning (RL) has emerged as the dominant fine-tuning paradigm, underpinning many state-of-the-art LLMs. In contrast, evolution strategies (ES) has largely been overlooked due to the widespread belief that it does not scale to modern model sizes. This paper overturns this assumption by demonstrating the first successful application of ES to full-parameter fine-tuning of LLMs at the billion-parameter scale, without dimensionality reduction. ES can indeed search over extremely high-dimensional parameter spaces and outperform established RL implementations across multiple axes, including improved tolerance to long-horizon and delayed rewards, robustness across diverse base LLMs, reduced susceptibility to reward hacking, and improved training stability. These findings suggest that ES is not merely a viable alternative to RL, but a fundamentally different and powerful backpropagation-free post-training paradigm that opens a new direction for LLM fine-tuning beyond current RL-based approaches.