Evolution Strategies

Also known as ES

Evolution strategies (ES) optimize by evaluating perturbed candidates and using their rewards or ranks to estimate which parameter changes are useful, without backpropagation. Methods such as CMA-ES and natural evolution strategies adapt mutation scales or covariance, while low-rank and cooperative variants reduce the cost of searching large spaces. They are used for black-box engineering and reinforcement learning, as well as language-model fine-tuning, prompt search, and agent training where rewards may be delayed or gradients unavailable. A central tension is balancing broad exploration and diverse solutions against evaluation cost, noisy feedback, and stability; matching gradient-based methods on task scores does not necessarily mean similar effects on other capabilities or knowledge.

Latest papers

34 papers6 papers in the last four weeks, up 100% on the four weeks before. 0.0% of all new papers.

Center-of-Mass Interpretation of Evolution Strategies
Oct 26, 2026Akshat GuptaEvolution Strategies Evolutionary Optimization
UC Berkeley
The Modular CMA-ES: A Framework for Modern Evolution Strategies
Oct 7, 2026Jacob de Nobel, Diederick Vermetten, Anna V. Kononova +2Evolution Strategies Covariance Matrix Adaptation Evolution Strategy
DP-ES: Differentially Private Evolution Strategies for Prompt Optimization
Oct 5, 2026Ziniu Liu, Aiping Li, Yue Han +5Large Language Model-Guided Optimization Evolution Strategies
National University of Defense Technology · CRRC Zhuzhou Electric Locomotive Research Institute Co., Ltd., China Academy of Railway Sciences
DART-ES: Difficulty-Aware Reweighting and Targeted Replay for Fine-Tuning LLMs with Evolution Strategies
Oct 4, 2026Zhishen Sun, Hongzhan Wang, Sizhe Dang +2LLM Fine-Tuning Evolution Strategies
Xi’an Jiaotong University · SGIT AI Lab
Asynchrony Is Nearly Free for Evolution Strategies on Long-Horizon LLM Agentic Tasks
Oct 3, 2026William Hoy, Jingxuan Fan, Nurcin Celik +1Evolution Strategies RL Post-Training
University of Miami · Harvard University
Continual Reinforcement Learning with Neuroevolution
Oct 1, 2026Eleni Nisioti, Andrea Cossu, Kathrin Korte +1Neuroevolution Loss of Plasticity
IT University of Copenhagen · University of Pisa · Sakana AI
Online Evolution Strategy for Flow-Matching VLA Policies via Self-Supervised Trajectory Distribution Optimization
Sep 30, 2026Gongxin Yao, Yongsheng Zhao, Jiayin Deng +4Flow Matching Evolution Strategies
China Mobile (Hangzhou) Information Technology Co., Ltd., Hangzhou, 311121, China
Hill Sampling for Test-Time Scaling: A Simple and Better Alternative to Repeated Sampling, Evolution, and Training
Sep 22, 2026Jacob Beck, Philip V. Ogren, Ari KobrenInference-Time Search Evolution Strategies
Oracle
EGGROLL, Unrolled: Understanding and Improving Low-Rank Evolution Strategies at Scale
Sep 10, 2026Ege C. Kaya, Abolfazl HashemiEvolutionary Optimization Evolution Strategies
Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA
Flawed in Nature, Perfect through Evolution
Aug 31, 2026J. M. Diederik KruijssenEvolution Strategies Adaptive Learning
Allora Foundation
Coverage, Not Credit: Failure-Credit Routing of Zeroth-Order Perturbation Budgets Does Not Improve On-Pool Sample Efficiency for LLM Agents
Aug 28, 2026Yuxu GeLLM Agent Training Fine-Grained Credit Assignment
University of York
Understanding Evolution Strategies for LLM Reasoning: Broader Reasoning Coverage than GRPO
Aug 27, 2026Yunpeng Ba, Zhi Zheng, Yue Xie +7Evolution Strategies LLM Post-Training
Southern University of Science and Technology · National University of Singapore · Harbin Institute of Technology, Weihai +2
ES-AHD: An Evolution Strategy Framework for Automatic Heuristic Design
Aug 26, 2026Yutao Lai, Kezhao Lai, Hai-Lin Liu +2Automated Heuristic Design Large Language Model-Guided Optimization
School of Mathematics and Statistics Guangdong University of Technology Guangzhou, China · School of Computer Science and Technology Xidian University Xi’an, China · School of Systems Science Beijing Normal University Beijing, China
Integer Natural Evolution Strategies
Aug 24, 2026Jacob de Nobel, Diederick Vermetten, Hao Wang +3Evolution Strategies Natural Gradient Methods
Leiden University, Leiden, The Netherlands · Sorbonne Université, CNRS, LIP6, Paris, France · Tel-Hai - University of Kiryat Shmona in the Galilee, Israel +1
Agentic ESOpt: Fine-Tuning Long-Horizon LLM Agents with Minimal GPU Requirements
Aug 18, 2026Zhi Zheng, Rongsheng Chen, Yunpeng Ba +3LLM Agent Training Long-Horizon LLM Agents
National University of Singapore · Southern University of Science and Technology · Oxford
Beyond the Best Guess: Improving LLM Solution Coverage with Evolution Strategies
Aug 13, 2026Conor F. Hayes, Elliot Meyerson, Kajetan Schweighofer +4Evolution Strategies LLM Post-Training
1Cognizant AI Lab, San Francisco · 2The University of Texas at Austin, Austin
Cooperative Coevolution for Resource-Constrained Agentic LLM Post-Training
Aug 3, 2026Zhiyuan Wang, Shengcai Liu, Jiahao Wu +5Evolutionary Optimization Evolution Strategies
Guangdong Provincial Key Laboratory of Brain-inspired Intelligent Computation, Department of Computer Science and Engineering, Southern University of Science and Technology · Hong Kong Polytechnic University · Hong Kong University of Science and Technology +2
Accelerating Evolutionary Strategy via Rao-Blackwellizing Realization of Uncertain Input
Aug 3, 2026So Nakashima, Tetsuya J. KobayashiStochastic Optimization Evolution Strategies
Institute of Industrial Science The University of Tokyo · Institute of Industrial Science, The University of Tokyo · Universal Biology Institute, The University of Tokyo
Neural Operator-enabled Topology-informed Evolutionary Strategy for PDE-Constrained Optimization
Jul 8, 2026Xiangming Huang, Guannan Zhang, Lu Lu +1Evolution Strategies Constrained Optimization
Bridging Spherical Black-Box Optimizers
Jun 24, 2026Johannes Ackermann, Stefano PeluchettiEvolutionary Optimization Black-Box Optimization
The University of Tokyo · Sakana AI
Model Merging to Evolution: Parameter Space Exploration for Expert Models
Jun 17, 2026Chao Wang, Yuchen Guo, Zheng Tan +4Evolutionary Optimization Evolution Strategies
School of Artificial Intelligence, Xidian University, Xi’an, China · School of Computer Science, University of Birmingham, Birmingham, UK · Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, China +3
Runtime Analysis of the $(μ+ 1)$ -ES in a Homogenous Progress Model
Jun 11, 2026Johannes Lengler, Raghu Raman RaviEvolutionary Optimization Evolution Strategies
Eidgenössische Technische Hochschule Zürich, Switzerland
Beyond Static Evaluation: Co-Evolutionary Mechanisms for LLM-Driven Strategy Evolution in Adversarial Games
Jun 9, 2026Haoran Li, Zengle Ge, Ziyang Zhang +10Game-Playing Agents Evolutionary Optimization
University of Chinese Academy of Sciences · Famou Agent Team, Baidu AI Cloud · The University of Sydney, Australia +3
Depth over Fidelity in Fixed-Budget Noisy Evolution Strategies
Jun 4, 2026Sichen Wang, Zhipeng LuEvolutionary Optimization Black-Box Optimization
Department of Engineering, Shenzhen MSU-BIT University, Shenzhen, China · Guangdong Laboratory of Machine Perception and Intelligent Computing, Shenzhen, China
Overcoming Forgetting in LLM Fine-Tuning with Evolution Strategies
May 28, 2026Kajetan Schweighofer, Conor F. Hayes, Roberto Dailey +2Continual Learning for LLMs Evolutionary Optimization
Cognizant AI Lab · UT Austin & Cognizant AI Lab
Convergence Analysis of Evolution Strategies for Mixed-Integer Optimization
May 20, 2026Ryoki Hamano, Kento Uchida, Shinichi ShirakawaEvolutionary Optimization Evolution Strategies
CyberAgent · Yokohama National University
From Mean-Field Limits to Semiclassical Concentration: Global Convergence of the Canonical Evolutionary Strategy
May 19, 2026Matías Neto, Nicolás Garay, Luis Martí +1Dynamical Systems Evolutionary Optimization
Inria Chile Research Center, Av Apoquindo 2827, Las Condes, RM, Chile · Departamento de Ingeniería Matemática, Universidad de Chile, Santiago, Chile
Gradient-Free Training of Spiking Neural Networks via Low-Rank Evolution Strategies
May 14, 2026Dhruv Patankar, Sachit Ramesha GowdaGradient-Free Optimization Evolutionary Optimization
Shunya Research
RCMAES: A Robust CMA-ES Variant for CEC2026 Competition
Apr 29, 2026Khoirul Faiq Muzakka, Sören Möller, Martin FinsterbuschEvolutionary Optimization Black-Box Optimization
Institute of Energy Materials and Devices (IMD-2), Forschungszentrum Jülich GmbH, Germany
Matching Accuracy, Different Geometry: Evolution Strategies vs GRPO in LLM Post-Training
Apr 2, 2026William Hoy, Binxu Wang, Xu PanEvolution Strategies RL Post-Training
Department of Industrial and Systems Engineering, University of Miami · Kempner Institute, Harvard University · Harvard University

Oct 26, 2026J/K move · Enter open · S save

Center-of-Mass Interpretation of Evolution Strategies

Akshat Gupta

UC Berkeley

Evolution Strategies Evolutionary Optimization

Open paper AskPDF arXiv

Evolution strategies (ES) update a model by sampling a population of perturbed copies, scoring each one, and moving in the reward-weighted direction of the perturbations. This update is usually presented as an estimate of a smoothed gradient. We present a geometrical interpretation of this update instead. Treat each perturbed model as a particle and its reward as the particle's mass. Before scoring, every particle has the same mass and the population balances at its centroid. Once rewards are assigned, it balances at its reward-weighted center of mass instead. We show that the mean-subtracted ES update is exactly this displacement, scaled by a scalar factor that depends on the mean reward, for any finite population. The physical reading needs nonnegative rewards, which can always be arranged by adding a constant to every reward without changing the update. In the limit of a large population or under antithetic sampling, the centroid sits on the model itself, so ES has an even simpler geometric interpretation: from its current location, the model moves towards the reward-weighted center of mass of its own population. The same picture explains what subtracting the mean reward does: it changes the point from which the displacement is measured, from the model to the sampled centroid. Our contribution is an intuitive, geometric way to visualize an ES update, exact for any finite population.