Evolution Strategies

Also known as ES

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4 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

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Latest papers 23

Oct 7, 2026cs.NE

The Modular CMA-ES: A Framework for Modern Evolution Strategies

Since their introduction, modern evolution strategies, such as the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), have become established as powerful methods for continuous black-box optimization. This success has led to a wide range of proposed modifications, each designed to improve performance or behavior in specific optimization scenarios. However, because these developments have largely been introduced and studied in isolation, their interactions remain comparatively underexplored. In this paper, we present the Modular CMA-ES (ModCMA), a configurable framework that integrates a wide range of mechanisms from modern evolution strategies within a single implementation. By decomposing CMA-ES into modules with interchangeable options for sampling, selection and recombination, step-size adaptation, matrix adaptation, and restarting, ModCMA enables systematic exploration of a large design space of modern evolution strategies and facilitates the construction, comparison, and automated configuration of new algorithm variants. We illustrate the benefits of this modular approach through two example studies. First, we compare several matrix-adaptation mechanisms in terms of their computational cost and optimization performance. Second, we use automated algorithm configuration to specialize ModCMA to individual benchmark problems and analyze the resulting configurations. Together, these examples demonstrate how the framework can be used both to study individual algorithmic design choices and to explore their combinations in a systematic and reproducible manner.

Jacob de Nobel, Diederick Vermetten, Anna V. Kononova +2

Evolution Strategies Covariance Matrix Adaptation Evolution Strategy Black-Box Optimization

Oct 5, 2026cs.CR

DP-ES: Differentially Private Evolution Strategies for Prompt Optimization

Token-level differentially private (DP) prompt optimization methods such as DP-OPT can become unstable under tight privacy budgets: on GSM8K, DP-OPT obtains

49.5\pm28.5\%

across 30 runs, and a logged search trajectory reveals prompt-template drift and noise-sensitive irreversible choices. We diagnose these as structural consequences of greedy token-by-token construction over privately aggregated counts. We then propose DP-ES (Differentially Private Evolution Strategies), a structurally cleaner alternative that maintains a population of full prompts, mutates them via LLM calls that never access the private dataset, and spends privacy only on sampled-Gaussian evaluation; deterministic or Gumbel-smoothed selection is post-processing. Under a conservative

(\varepsilon\leq1.0,δ=10^{-5})

guarantee, DP-ES achieves 88.1% on GSM8K (+38.6 pp over DP-OPT, approximately 9 times lower standard deviation), 99.7% on MedQA, 73.5% on BANKING77, and 86.8% on Alpaca. It is also 2.5 times faster in wall-clock time and uses 3.3 times fewer logged private-data call groups than DP-OPT. Selection and population ablations, implementation-level noise checks, and a 200-profile exact-match memorization stress test complement the formal guarantee. Scope: Our experiments establish optimization robustness under DP noise, especially where prompt structure is critical; end-to-end validation on genuinely sensitive, non-saturated deployment data remains future work.

Ziniu Liu, Aiping Li, Yue Han +5

National University of Defense Technology · CRRC Zhuzhou Electric Locomotive Research Institute Co., Ltd., China Academy of Railway Sciences

Large Language Model-Guided Optimization Evolution Strategies Automatic Prompt Optimization Privacy-Preserving ML Differential Privacy

Oct 1, 2026cs.NE

Continual Reinforcement Learning with Neuroevolution

Despite many studies about causes and remedies of plasticity loss in Reinforcement Learning (RL) under continual task changes, no RL method has yet consistently achieved a good balance between adaptation and forgetting. Here we turn to an alternative optimization paradigm, neuroevolution (NE): algorithms that search directly in weight space through mutation and selection over a population of neural networks. Across a wide array of environments and environmental changes, with policies ranging from a few hundred parameters to million-parameter networks, we compare evolution strategies (ES) and genetic algorithms (GAs) against state-of-the-art continual RL variants and population-based RL. ES most consistently achieves a good stability-plasticity trade-off, while the GA is the most plastic method but forgets more than ES. To explain this, we study the return landscape around each method's solutions. ES finds the widest neighborhoods, i.e.\ regions of weight space in which perturbed policies still solve the task, and the size of the overlap between the neighborhoods of consecutive tasks correlates with a method's stability-plasticity trade-off. Rewarding behavioral diversity in a GA through novelty search makes the population even more plastic, at the cost of forgetting. Finally, symptoms of plasticity loss commonly reported in RL do not transfer to NE. Overall, these results establish NE as a competitive alternative to RL under continual task changes, and suggest that training under perturbations in weight space may be a useful mechanism for continual learning more broadly.

Eleni Nisioti, Andrea Cossu, Kathrin Korte +1

IT University of Copenhagen · University of Pisa · Sakana AI

Stability-Plasticity Dilemma Loss of Plasticity Evolution Strategies Continual RL Genetic Algorithms Neuroevolution

Sep 30, 2026cs.RO

Online Evolution Strategy for Flow-Matching VLA Policies via Self-Supervised Trajectory Distribution Optimization

Vision-Language-Action (VLA) models based on generative frameworks, such as Flow Matching, have recently achieved impressive performance in robotic manipulation. Unlike deterministic policies, Flow Matching enables VLA models to learn conditional action trajectory distributions, where latent noise vectors induce different actions under the same task scenario. However, we observe that these distributions are often ill-formed, with successful and failed behaviors coexisting while considerable probability mass remains in unfavorable regions. To this end, we propose Online-ES, an online adaptation framework for Flow Matching VLAs based on Evolution Strategy (ES), which refines the learned action trajectory distribution through interaction feedback. Instead of pruning the latent noise space, our method performs evolutionary exploration directly in the action trajectory space, where diverse trajectories generated by Flow Matching provide candidate solutions for adaptation. By perturbing sampled trajectories and evaluating their execution outcomes, we derive a self-supervised MSE objective that transfers the evolution direction from trajectory space into model parameter space. Mathematically, we prove that the proposed objective provides an unbiased estimator of the optimal evolution direction. Moreover, we also incorporate failure experiences as negative feedback to regularize the evolution direction, steering the policy away from previously explored failure regions. Experiments in both simulation and real-world environments demonstrate that Online-ES achieves policy improvement comparable to reinforcement fine-tuning, without learning a value model or computing advantages.

Gongxin Yao, Yongsheng Zhao, Jiayin Deng +4

China Mobile (Hangzhou) Information Technology Co., Ltd., Hangzhou, 311121, China

Flow Matching Evolution Strategies Robotic Manipulation Vision-Language-Action Models Test-Time Adaptation of VLA Models

Sep 22, 2026cs.LG

Hill Sampling for Test-Time Scaling: A Simple and Better Alternative to Repeated Sampling, Evolution, and Training

Large language models (LLMs) can improve solutions to verifiable scientific and algorithmic problems by spending additional computation at test time. Recent systems achieve strong results with increasingly elaborate evolutionary search harnesses or by updating model parameters during test-time training. We ask how much of this machinery is necessary. We introduce Hill Sampling, a simple procedure that repeatedly samples candidate program edits from a frozen LLM, retains the best program found so far, and conditions all subsequent samples on that program. We evaluate the method on circle packing, sums/differences of sets, and Erdos' minimum-overlap problem using three open-weight models. Hill Sampling sets a new state of the art on circle packing among published methods, improves over the AlphaEvolve reference on Erdos' minimum-overlap problem, and achieves strong results on sums and differences of finite sets. The circle-packing and Erdos results require only hours of wall-clock time on eight NVIDIA H100 GPUs. To our knowledge, we also conduct, the largest study, by parameter count, of evolution strategies (ES) applied directly to LLM weights at test time. Surprisingly, learning the weights is worse than setting the ES learning rate to zero: at zero learning rate, the method is still searching in weight space through fixed random perturbations. Those perturbations can help exploration, but randomness from token sampling is stronger still, and repeated sampling remains substantially weaker than Hill Sampling. These results suggest a simple test-time compute allocation strategy: repeatedly sample edits to the best verified solution found so far, before introducing additional complexity such as adding archives, diversity mechanisms, evolutionary scaffolds, or test-time parameter learning.

Jacob Beck, Philip V. Ogren, Ari Kobren

Oracle

Inference-Time Search Evolution Strategies Test-Time Scaling Program Synthesis Large Language Model-Guided Scientific Discovery

Sep 12, 2026cs.LG

EGGROLL, Unrolled: Understanding and Improving Low-Rank Evolution Strategies at Scale

EGGROLL makes evolution strategies (ES) practical for LLMs by replacing dense Gaussian weight perturbations with low-rank Gaussian products, often of rank one. This choice is computationally attractive but geometrically severe: each rank-one perturbation lies in a zero-volume subset of the ambient matrix space, despite having identity covariance. We characterize the mean EGGROLL update field at finite rank and nonzero perturbation radii, then analyze the error of its finite-population estimator. The population field is obtained by applying an explicit resolvent to the gradient of the objective smoothed by the perturbations. We show that the resolvent can introduce a nonconservative component and can reverse the local stability of an optimum. EGGROLL is nevertheless exact on every quadratic objective at every rank and radius. For smooth objectives, its first local finite-rank correction is

O(\sigma^2/r)

, and nonasymptotic bounds control the resulting field error under smoothness assumptions. Under a local affine model, rank-one perturbations increase the variance of the gradient estimator by only

\frac{2(m+n+1)}{mn+1}

relative to dense Gaussian ES, or

0.098\%

for a

4096\times4096

matrix. We then introduce LOO-ROLL, a leave-one-out estimator that preserves the finite-rank population field while replacing EGGROLL's two antithetic evaluations per direction by one. At equal evaluation cost, LOO-ROLL halves estimator MSE in transformer blocks. At matched wall time across ten post-training settings and models up to 8B parameters, LOO-ROLL improves seven outcomes in individual paired tests, with no significant loss. On the GSM8K test set, accuracy increases from

38.1\%

to

63.0\%

at 0.6B and from

65.9\%

to

80.0\%

at 8B. Transformer measurements recover the predicted finite-rank variance, while the rank comparisons show no reproducible reward-based advantage for rank eight.

Ege C. Kaya, Abolfazl Hashemi

Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA

Evolutionary Optimization Evolution Strategies LLM Post-Training

Aug 31, 2026cs.LG

Flawed in Nature, Perfect through Evolution

The performance of artificial intelligence (AI) and machine learning (ML) models degrades when the problem they were trained on drifts. This is a near-universal feature of real-world problems, which often change unpredictably. Biological evolution has achieved intelligence by overcoming this obstacle through natural selection acting on heritable variation. AI/ML techniques have long incorporated forms of natural selection, but it has been challenging to maintain model diversity as optimization naturally drives convergence. Here we show that a swarm of AI/ML models subjected to deliberate mutations of their model coefficients away from optimality can reliably and sustainably improve performance in changing environments by acting as a statistical hedge against non-stationarity. We call this mechanism 'Flawed in Nature, Perfect through Evolution', reflecting that the collective performance gain goes at the expense of individual performance. We prove via four theorems that the resulting regret reduction is guaranteed under general conditions, establishing the Flawed-in-Nature mechanism as a generalizable design principle for AI/ML systems. We validate these results on synthetic linear regression tasks, demonstrating that the mutated swarm delivers the best model in

\sim80\%

of environment changes and that inference synthesis successfully translates this individual advantage into a collective one. The mechanism proves to be most effective when the mutation drift rate matches the drift rate of the environment. We outline a simple, adaptive controller that enables practical applications by tuning the mutation drift rate to match the unknown drift rate of the environment. The close analogy of the Flawed-in-Nature mechanism to biological evolution suggests it may have been a critical missing ingredient for the organic discovery of AI forms that more closely mimic biological intelligence.

J. M. Diederik Kruijssen

Allora Foundation

Evolution Strategies Adaptive Learning

Aug 13, 2026cs.AI

Beyond the Best Guess: Improving LLM Solution Coverage with Evolution Strategies

Large Language Models (LLMs) are increasingly deployed in discovery domains such as math and science. The usual approach is to present the problem to the model and use its answer as the proposed solution. However, beyond this best guess, discovery can be enhanced by increasing test-time compute. In a process called pass@k, the model is allowed to explore the solution space and generate diverse candidate solutions. Unfortunately, the standard approach to post-training LLMs through Reinforcement Learning (RL) may limit pass@k: the model's output distribution narrows around high-reward outputs, causing the solution coverage to collapse. The alternative is to use Evolution Strategies (ES), a population-based, gradient-free post-training method that optimizes directly in weight space through random perturbations. As this paper shows, ES achieves consistently higher pass@k than RL and produces a broader output distribution with greater solution coverage. This coverage in turn makes it possible to achieve better results in e.g. standard math benchmarks. Thus, ES provides a better foundation for post-training in discovery problems and other domains where diverse solution coverage is critical.

Conor F. Hayes, Elliot Meyerson, Kajetan Schweighofer +4

1Cognizant AI Lab, San Francisco · 2The University of Texas at Austin, Austin

Evolution Strategies LLM Post-Training Large Language Model-Guided Scientific Discovery

Aug 3, 2026cs.AI

Cooperative Coevolution for Resource-Constrained Agentic LLM Post-Training

Tool-using large language model (LLM) agents produce long, multi-turn trajectories, making gradient-based post-training memory-intensive. Evolution strategies (ES) enable memory-efficient full-parameter post-training without backpropagation and can eventually match the performance of gradient-based reinforcement learning (RL). However, resource-constrained settings typically offer only a few GPUs, so the high GPU-hour requirements of ES translate into prohibitively long training times. To address this, we introduce Cooperative Parameter-subspace Evolution Strategy (CoPES), a cooperative coevolutionary method that decomposes the full parameter space into lower-dimensional subspaces and searches over them cooperatively to improve optimization efficiency. We post-train a Qwen3.5-4B tool-using agent for the math task and evaluate it on five benchmarks of varying difficulty. Under the GPU-hour budget of full-parameter GRPO's best validation checkpoint, CoPES recovers 92% of GRPO's validation-accuracy gain, versus 67% for standard ES, while its theoretical GPU memory requirement is less than one-eighth that of full-parameter GRPO. It consistently outperforms standard ES and LoRA-based GRPO on all evaluated pass@k metrics across the five benchmarks. Additional experiments further show the advantage of CoPES on the question-answering task. These results demonstrate an improved trade-off between memory requirements and training time for agentic LLM post-training under resource constraints. The code is open-sourced in https://github.com/MetaronWang/CoPES

Zhiyuan Wang, Shengcai Liu, Jiahao Wu +5

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

Evolutionary Optimization Evolution Strategies LLM Post-Training Language Model Post-Training RL for LLM Agents

Aug 3, 2026math.OC

Accelerating Evolutionary Strategy via Rao-Blackwellizing Realization of Uncertain Input

We investigate Optimization under Input Uncertainty (OIU), in which the input to the objective function, rather than the objective function itself, is subject to uncertainty. OIU appears in manufacturing processes with production tolerance, control of physical systems with actuation noise, Mixture of Experts, and Reinforcement Learning (RL). Most of the existing approaches solve OIU by using the value of the objective function but discard the information of the realized input, even though the realized input is observable in various applications. The question here is whether the discarded information of the realized input is useful to accelerate the optimization process. We affirmatively answer this question for Evolutionary Strategy (ES) by theoretically showing that the information of the realized input can reduce the variance of the gradient estimator via Rao-Blackwellization. Using the Rao-Blackwellized gradient estimator, we propose Phenotype-Accelerated Evolutionary Strategy (PAES), which is a refinement of ES for OIU. Numerical experiments show that PAES converges faster than the usual ES from simple continuous optimization problems to RL benchmarks.

So Nakashima, Tetsuya J. Kobayashi

Institute of Industrial Science The University of Tokyo · Institute of Industrial Science, The University of Tokyo · Universal Biology Institute, The University of Tokyo

Stochastic Optimization Evolution Strategies Variance Reduction

Jul 8, 2026cs.LG

Neural Operator-enabled Topology-informed Evolutionary Strategy for PDE-Constrained Optimization

The inverse design of physical systems governed by partial differential equations is computationally demanding due to the high dimensionality and non-convexity of design spaces. Generative models for inverse design often lack robustness and transferability, whereas evolutionary strategies are robust but struggle in high-dimensional spaces. This paper introduces a Neural Operator-enabled Topology-informed Evolutionary Strategy (NOTES) that integrates dimensionality reduction, representation learning, and evolutionary optimization for efficient and transferable inverse design. NOTES couples a DeepONet-based neural operator with the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to perform global optimization in a compact latent space that encodes topology-aware priors while discovering high-performance designs for unseen operating conditions. Applied to nanophotonic beam-deflector inverse design governed by Maxwell's equations, NOTES reduces the design dimensionality from 256 to 25 and consistently achieves over 95 percent efficiency, outperforming CMA-ES, topology optimization, and other baselines. Applied to structural optimization, NOTES discovers designs that achieve compliance down to 246. By decoupling topology learning of a DeepONet from the governing physics in a PDE solver, NOTES provides a flexible and transferable framework for the inverse design of physical systems.

Xiangming Huang, Guannan Zhang, Lu Lu +1

Evolution Strategies Constrained Optimization Inverse Design

Jun 24, 2026cs.LG

Bridging Spherical Black-Box Optimizers

When gradient information is unavailable, black-box optimization (BBO) methods provide a practical alternative. While Evolution Strategies (ES), Consensus-Based Optimization (CBO), Optimization via Integration (OVI), and related methods have each been studied independently, their connections remain underexplored. We unify these approaches within a common theoretical framework, revealing that they differ primarily in two design choices: fitness aggregation (controlling sharpness preference) and consensus scope (controlling modality). Leveraging these insights, we introduce hybrid optimizers that interpolate between existing methods. Our ES-OVI hybrid allows explicit control over the preference for flat minima, enabling a trade-off between performance and robustness in continuous control tasks. Our CBO-OVI hybrids combine the higher-dimensional efficiency of parametric methods with the multimodal capabilities of particle-based approaches, achieving competitive results on language model merging under limited evaluation budgets. We validate our methods on standard BBO benchmarks and higher-dimensional locomotion tasks, demonstrating that the hybrid methods can outperform their constituent algorithms.

Johannes Ackermann, Stefano Peluchetti

The University of Tokyo · Sakana AI

Evolutionary Optimization Black-Box Optimization Evolution Strategies

Jun 17, 2026cs.NE

Model Merging to Evolution: Parameter Space Exploration for Expert Models

Model merging integrates the capabilities of multiple expert models to create strong models for multiple tasks without additional training, thereby reducing computational resource requirements. However, existing methods operate within the convex combination space of expert models, failing to explore high-performance regions outside this space. This paper proposes the MERGEvolve framework, which unifies model merging and evolution within an evolution strategy by treating the merged model as the initialization for evolutionary exploration of the parameter space. During the merging phase, expert models act as deterministic sources to build a strong initial point. The evolution phase then explores the parameter space using random noise. Theoretical analysis shows that MERGEvolve explores regions outside the convex combination space. Extensive experiments on single-task and multi-task benchmarks demonstrate that MERGEvolve consistently achieves performance competitive with advanced model merging baselines. Ablation studies confirm that a high-quality initial point is critical for efficient exploration of the parameter space.

Chao Wang, Yuchen Guo, Zheng Tan +4

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

Evolutionary Optimization Evolution Strategies Model Merging

Jun 11, 2026cs.NE

Runtime Analysis of the $(μ+ 1)$ -ES in a Homogenous Progress Model

We introduce a new simple model to study the fitness progress of Evolution Strategies (ES) in generic problems. In this model, we bypass the underlying fitness landscape and assume that the mutation of any individual produces an offspring whose fitness relative to the parent is given by an invariant distribution

Z

, such as a mean-shifted Gaussian. This serves as a prototypical model for the optimisation landscape when an evolution algorithm operates far from the global optimum. This simple model can be used to approximate the optimisation process for problems where it is intractable to model the exact fitness function, including tasks such as hyperparameter tuning in machine learning models. We rigorously analyse the expected growth rate

\mathcal{R}_μ

of the continuous steady-state

(μ+1)

-ES in this model. Unlike comma-selection strategies, the steady-state

(μ+1)

-ES maintains overlapping generations, introducing complex mathematical dependencies among surviving parents that make it harder to analyse. We give a general technique to analyse the the

(μ+ 1)

-ES by constructing modified processes whose growth rates provably sandwich that of the original process. These modified processes are then easier to analyse but still close enough to the true process to give a tight bound on the expected growth rate. When

Z = \mathcal{N}(-δ, 1)

and

μ\le e^δ

, we show that

\mathcal{R}_μ = \frac{\log^{1 + o(1)} μ}μ \mathcal{R}_1

.

Johannes Lengler, Raghu Raman Ravi

Eidgenössische Technische Hochschule Zürich, Switzerland

Evolutionary Optimization Evolution Strategies Runtime Analysis of Evolutionary Algorithms

Jun 9, 2026cs.AI

Beyond Static Evaluation: Co-Evolutionary Mechanisms for LLM-Driven Strategy Evolution in Adversarial Games

Recent advances in LLM-driven code evolution have enabled automated discovery by iteratively generating and improving programs. However, applying these methods to adversarial multi-agent games introduces a fundamental challenge: the evaluation landscape shifts as strategies improve, causing fixed evaluators to become unreliable and evolution to stagnate. We propose three mechanisms to address this challenge: evaluator co-evolution, which incorporates discovered champions into the opponent pool; hierarchical deep evaluation, which replaces noisy few-game scores with statistically reliable assessments; and weakness pressure, which dynamically up-weights the most difficult opponents to break through plateaus. We implement these mechanisms within FAMOU, a framework built upon the same foundation-model code-evolution paradigm as OpenEvolve and ShinkaEvolve. On the MCTF 2026 3v3 maritime capture-the-flag task, FAMOU consistently outperforms both baselines under two backbone LLMs, achieving the highest combined score (0.526) and the best generalization to unseen opponents (61.7% win rate), while ablations confirm that each mechanism contributes to performance. Notably, the LLM mutation process generates tactical structures entirely absent from the seed strategies -- including lookahead search and adaptive interception -- demonstrating that code-level evolution can produce nontrivial algorithmic innovations in adversarial settings. The FAMOU-evolved strategy further achieved 1st place in the hardware round-robin and 3rd in simulation at the AAMAS 2026 MCTF Competition, validating its real-world transferability. The optimized implementation and corresponding evaluation codes developed through our evolutionary process are available at: https://github.com/1xiangliu1/FAMOU-CoEvo

Haoran Li, Zengle Ge, Ziyang Zhang +10

University of Chinese Academy of Sciences · Famou Agent Team, Baidu AI Cloud · The University of Sydney, Australia +3

Game-Playing Agents Evolutionary Optimization Large Language Model-Guided Optimization Evolution Strategies Self-Evolving Agents

Jun 4, 2026cs.NE

Depth over Fidelity in Fixed-Budget Noisy Evolution Strategies

Noisy evolution strategies under fixed evaluation budgets face a depth-fidelity trade-off: spending evaluations to denoise intra-generation rankings reduces the number of distribution updates the optimizer can execute. We argue for depth over fidelity and propose probabilistic elite membership (PEM), which replaces hard rank-based weights in evolution strategies with conditional expected rank weights that integrate over ranking uncertainty. PEM preserves the conditional mean update while reducing conditional update dispersion, a Rao-Blackwellization of the noisy rank-based step. We instantiate PEM via residual bootstrapping (RB-PEM) with capped per-generation overhead, complemented by an adaptive probe-and-switch mechanism for low-noise regimes. Across the COCO bbob-noisy suite and external tasks including RL policy search and hyperparameter optimization, RB-PEM achieves consistent gains in high-misranking, budget-constrained settings.

Sichen Wang, Zhipeng Lu

Department of Engineering, Shenzhen MSU-BIT University, Shenzhen, China · Guangdong Laboratory of Machine Perception and Intelligent Computing, Shenzhen, China

Evolutionary Optimization Black-Box Optimization Evolution Strategies Variance Reduction

May 28, 2026cs.LG

Overcoming Forgetting in LLM Fine-Tuning with Evolution Strategies

Evolution Strategies (ES) has recently emerged as a competitive alternative to reinforcement learning (RL) for large language model (LLM) fine-tuning, offering advantages through simplicity, scalability, and inference-only training. However, recent work suggests that ES fine-tuning on new tasks may induce forgetting of prior tasks. First, this paper shows that prior task forgetting (1) is better characterized as performance drift rather than irreversible forgetting, with prior-task performance often recovering during ES training; and (2) is not a specific failure mode of ES, but can also arise for fine-tuning with RL methods. Second, it analyzes when and why such drift arises, highlighting its dependence on ES training dynamics, particularly random walk behavior in weakly constrained directions of the weight space. Third, based on these insights, it introduces Anchored Weight Decay (AWD) as a parameter-space regularization technique that constrains optimization toward the initial model parameters. AWD effectively stabilizes prior-task performance while preserving target-task performance, achieving benefits comparable to large ES population sizes at much lower computational cost. Thus, contrary to previous beliefs, the paper shows that prior-task forgetting under ES is largely avoidable, positioning ES as a promising approach for continual learning in LLMs.

Kajetan Schweighofer, Conor F. Hayes, Roberto Dailey +2

Cognizant AI Lab · UT Austin & Cognizant AI Lab

Continual Learning for LLMs Evolutionary Optimization Evolution Strategies Catastrophic Forgetting

May 20, 2026cs.NE

Convergence Analysis of Evolution Strategies for Mixed-Integer Optimization

Mixed-integer extensions of evolution strategies (ES) that discretize selected coordinates of sampled continuous vectors often impose a lower bound on the standard deviation of integer variables to prevent premature convergence. While these methods show promising empirical results, this handling can slow the convergence of continuous variables, and its impact has lacked a clear theoretical account. In this paper, we provide a convergence analysis of evolution strategies for mixed-integer optimization, inspired by the drift analysis of the (1+1)-ES in the continuous domain. Specifically, we consider two (1+1)-ES variants for mixed-integer domains: (1+1)-LB-ES, which introduces a lower bound on the standard deviation for integer variables, and (1+1)-LUB-ES, which combines both lower and upper bounds to enhance the convergence of the continuous variables. Focusing on the optimization phase after the integer variables have been optimized, we rigorously analyze their convergence behavior on a benchmark function designed for mixed-integer domains. Our results show that (1+1)-LB-ES can suffer from premature convergence when the number of integer variables is large, while (1+1)-LUB-ES achieves linear convergence under suitable parameter settings. These findings provide theoretical insights into the impact of integer handling on convergence performance and guidance for the design of mixed-integer ES.

Ryoki Hamano, Kento Uchida, Shinichi Shirakawa

CyberAgent · Yokohama National University

Evolutionary Optimization Evolution Strategies Runtime Analysis of Evolutionary Algorithms

May 19, 2026cs.NE

From Mean-Field Limits to Semiclassical Concentration: Global Convergence of the Canonical Evolutionary Strategy

We address the issue of global convergence in stochastic continuous optimization. For that purpose, we formulate the Canonical Evolutionary Strategy (CES) as a controlled mathematical framework to analyze global convergence in evolutionary algorithms via the semiclassical limit of a Schr{ö}dinger-type replicator-mutator equation. We provide a rigorous hierarchy from a discrete individual-based dynamics to a deterministic mean-field limit, demonstrating that global convergence is governed by the principal eigenfunction of the underlying operator. This property, defined as Geometric Selection, naturally prioritizes robust, flat optima over narrow local traps, offering a mathematical justification for the ''survival of the flattest'' phenomenon. Moreover, unlike consensus-driven methods that are prone to premature variance collapse when the global minimizer resides outside the initial support, the replicator-mutator dynamics of CES facilitate intrinsic mass transport. High-dimensional benchmarks (d = 30) confirm this advantage, showing that CES achieves lower residual errors in shifted initialization scenarios where standard consensus-driven and gradient-based methods fail to migrate effectively. By shifting the focus from point-wise consensus to spectral concentration, our framework provides a robust theoretical foundation for global convergence in Evolution Strategies (ES) without the need for additional numerical heuristics.

Matías Neto, Nicolás Garay, Luis Martí +1

Inria Chile Research Center, Av Apoquindo 2827, Las Condes, RM, Chile · Departamento de Ingeniería Matemática, Universidad de Chile, Santiago, Chile

Dynamical Systems Evolutionary Optimization Evolution Strategies Global Optimization Stochastic Optimization Convergence Flat Minima

May 14, 2026cs.NE

Gradient-Free Training of Spiking Neural Networks via Low-Rank Evolution Strategies

Spiking Neural Networks (SNNs) offer compelling energy efficiency on neuromorphic hardware, yet their training remains challenging because the discrete spike threshold is non-differentiable. Surrogate-gradient methods sidestep this by approximating the derivative, but they impose backpropagation infrastructure that is incompatible with on-chip learning. Evolution Strategies (\es) are a natural gradient-free alternative, yet their computational cost scales with the number of parameters, making them impractical for large weight matrices. We present a method for training SNNs using EGGROLL, a low-rank factorisation of ES perturbations that reduces per-generation memory from

\mathcal{O}(mn)

to

\mathcal{O}(r(m{+}n))

. Combining EGGROLL with a Leaky Integrate-and-Fire SNN on N-MNIST, we demonstrate that gradient-free training achieves 79.21% test accuracy while reducing per-generation wall-clock time by 2.23

\times

relative to full-rank ES. Our results demonstrate EGGROLL is viable for SNN training, with a clear accuracy-speed tradeoff, compatible with training on neuromorphic hardware without surrogate gradients.

Dhruv Patankar, Sachit Ramesha Gowda

Shunya Research

Evolutionary Optimization Evolution Strategies Spiking Neural Networks Neuroevolution

Apr 29, 2026cs.NE

RCMAES: A Robust CMA-ES Variant for CEC2026 Competition

This paper proposes RCMAES, a novel variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for CEC benchmark optimization. RCMAES integrates a dimension-dependent nonlinear population-size reduction strategy with an adaptive restart mechanism within a pure CMA-ES framework. RCMAES is evaluated on three benchmark suites (CEC2017, CEC2020, and CEC2022) and compared with state-of-the-art DE algorithms as well as its closely related counterpart, BIPOP-aCMAES. Experimental results show that RCMAES achieves competitive and robust performance across all benchmarks.

Khoirul Faiq Muzakka, Sören Möller, Martin Finsterbusch

Institute of Energy Materials and Devices (IMD-2), Forschungszentrum Jülich GmbH, Germany

Evolutionary Optimization Black-Box Optimization Evolution Strategies Covariance Matrix Adaptation Evolution Strategy

Sep 29, 2025cs.LG

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

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.

Xin Qiu, Yulu Gan, Conor F. Hayes +6

Cognizant AI Lab, San Francisco, CA, USA · Massachusetts Institute of Technology, Cambridge, MA, USA · University of California, Los Angeles, Los Angeles, CA, USA +1

Fine-Tuning Evolutionary Optimization LLM Fine-Tuning Evolution Strategies RL Fine-Tuning

Jul 6, 2025cs.LG

ESSA: Evolutionary Strategies for Scalable Alignment

Online alignment of large language models (LLMs) is dominated by reinforcement learning from human feedback (RLHF) with gradient-based optimizers such as PPO or GRPO. While effective, these pipelines require backpropagation through long rollouts, gradient synchronization across devices, and careful hyperparameter tuning, all of which become increasingly costly at scale. We present ESSA (Evolutionary Strategies for Scalable Alignment), a gradient-free online alignment stage that follows supervised fine-tuning (SFT) and replaces the gradient loop with inference-only black-box search. ESSA optimizes only the singular values of low-rank adaptation (LoRA) factors after a short SFT warm-start, restricting the search to a compact, task-aligned subspace where evolutionary search is practical even for 72B-parameter models. Because the loop is inference-only, ESSA is compatible with INT4/INT8 weight quantization and reduces inter-GPU communication to a few bytes per iteration. Across instruction following (IFEval), preference-based assistant tuning (HelpSteer2, HH-RLHF), and mathematical reasoning (GSM8K, MATH500), ESSA matches or exceeds LoRA-GRPO in the reported LoRA comparisons; on GSM8K it also outperforms Online DPO and PPO, while remaining competitive with both methods on IFEval. At scale, ESSA reaches a fixed MATH500 accuracy on Qwen2.5-32B/PRM800K up to 7.8x faster than LoRA-GRPO on 128 GPUs.

Daria Korotyshova, Boris Shaposhnikov, Alexey Malakhov +7

T-Tech · Yandex

LLM Alignment Evolutionary Optimization Evolution Strategies