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Large Language Models Meet Bayesian Optimization: Towards Self-evolving Wireless Digital Twins

Yingzhuo Sun, Haoyun Li, Ming Xiao, Francisco J. Ferrao, Berna Ozbek

arXiv:2610.31192v1eess.SYcs.ITcs.SYmath.IT

TL;DR

Wireless digital twins often adapt within predefined learning or optimization structures that may not suit changing wireless tasks and operating conditions. The paper proposes an LLM-assisted BO framework that retains a stable BO workflow while adapting selected components using task context and accumulated experience. In a beam-selection simulation, the discovered kernel improves final BO performance over the strongest standard kernel baseline on both training and test tasks.

  • Problem

    Most existing AI-driven wireless digital twins adapt within predefined learning or optimization structures, which may be unsuitable as tasks and operating conditions change.

    Source: §I · p. 1

  • Method

    The framework uses an LLM to decide whether to retain or adapt selected BO components based on the current task and accumulated optimization experience, while BO provides the optimization backbone.

    Source: §I · p. 2, D. LLM-Driven BO Adaptation · p. 4

  • Results

    19.7% improvement in final BO performance on training tasks and 8.7% on test tasks over the strongest standard kernel baseline.

    Source: §VI · p. 6

  • Takeaways & Limitations

    The results provide a proof of concept for evolving a task-relevant BO component within a fixed BO structure for wireless optimization.

    Source: C. Performance Evaluation · p. 6, §VI · p. 6

    The simulation’s test tasks follow a similar underlying distribution to the training tasks, leaving adaptation under broader task changes for future work.

    Source: A. Adaptation under Task Changes · p. 6

Abstract

from arXiv · show

Wireless digital twins (DTs) are increasingly integrated with artificial intelligence to support online modeling, prediction, and network optimization. However, most existing approaches perform adaptation within predefined learning or optimization structures, which may become unsuitable when wireless tasks and operating conditions change. In this article, we investigate the integration of large language models (LLMs) and Bayesian optimization (BO) to extend wireless DTs from online adaptation towards algorithm-level self-evolution. We introduce an LLM-assisted BO framework in which BO provides a stable and sample-efficient optimization backbone, while the LLM determines whether selected BO components should be retained or adapted based on the current task and accumulated optimization experience. In simulations, we apply the framework to Gaussian process (GP) kernel discovery for a multi-user wireless beam-selection problem. Simulation results show that the LLM-discovered kernel improves the final BO performance by 19.7% on the training tasks compared with the strongest standard kernel baseline. The results demonstrate the potential of combining LLM flexibility with structured BO for self-evolving wireless DTs.

I. INTRODUCTION

Existing wireless digital twins adapt models, states, or policies within predefined structures, but changing tasks and conditions can make fixed optimization strategies unsuitable. The article proposes using LLMs to adapt selected BO components while preserving BO’s overall workflow.

I. INTRODUCTION

  • Changing wireless tasks, objectives, or network scales can make a fixed optimization strategy unsuitable, motivating adaptation of the optimization mechanism itself.The article distinguishes this from updating network states or policies within a predefined optimization structure.Source: §I · pp. 1–2
  • The framework lets an LLM use accumulated task, algorithm, and performance information to decide whether to retain or adapt the current BO configuration.When adaptation is needed, the LLM can generate new BO components and return them to the optimization loop.Source: §I · pp. 1–2
  • BO supports wireless digital twins through iterative surrogate updates and optimization decisions, but its initialization, surrogate, kernel, and acquisition function are usually predefined.BO has been applied to radio resource management, power control, beam alignment, and meta-optimization –.Source: §I · p. 1
  • The proposed LLM-assisted BO framework combines task interaction, BO execution, experience storage, prompt construction, adaptation decisions, and component generation in a closed loop.The study uses kernel discovery as a proof-of-concept example for evaluating whether generated BO components improve performance across wireless tasks.Source: §I · p. 2

II. FROM ONLINE ADAPTATION TO SELF-EVOLVING WIRELESS DIGITAL TWINS

LLMs and BO offer complementary capabilities for intelligent wireless optimization: LLMs contribute task understanding and algorithm generation, while BO provides structured, sample-efficient black-box optimization.

II. FROM ONLINE ADAPTATION TO SELF-EVOLVING WIRELESS DIGITAL TWINS

  • LLMs offer task-understanding and algorithm-generation capabilities, while BO provides a structured, sample-efficient approach to black-box optimization.Their different strengths and limitations motivate their integration for wireless digital twins.Source: §II · p. 2

A. Large Language Models for Wireless Intelligence

LLMs can interpret wireless task context and generate task-specific algorithms, but unconstrained algorithm generation can make optimization structures difficult to compare and reuse. BO offers a modular, sample-efficient framework for expensive wireless black-box problems, though its configuration is usually fixed in advance.

A. Large Language Models for Wireless Intelligence

  • LLM-generated algorithms can vary substantially across tasks, making optimization processes harder to constrain, compare, and reuse.The paper argues for retaining a stable optimization framework while allowing selected components to evolve.Source: A. Large Language Models for Wireless… · p. 2
  • LLMs can interpret task descriptions and contextual information, then generate task-specific decisions, algorithms, or executable code.The passage notes wireless uses in reasoning, configuration, optimization, and agent-based control –, as well as heuristic generation,.Source: A. Large Language Models for Wireless… · p. 2

B. Bayesian Optimization for Wireless Black-Box Problems

  • BO uses limited system observations to update a surrogate and select decisions sequentially for expensive wireless objectives.Its modular structure supports interpretable optimization and tracing behavior to individual algorithmic choices –.Source: B. Bayesian Optimization for Wireless… · p. 2
  • BO adapts its model to new observations but does not naturally adapt its own optimization structure when the objective, decision space, or scenario changes.Its configuration choices are commonly specified in advance.Source: B. Bayesian Optimization for Wireless… · p. 2

C. Combining LLMs and Bayesian Optimization

The paper combines LLM task-specific algorithm generation with BO’s stable workflow so selected components can evolve without redesigning the full optimization procedure. This provides a route toward wireless digital twins that adapt optimization components using the current task and accumulated experience.

C. Combining LLMs and Bayesian Optimization

  • Selected BO components can evolve through an LLM without redesigning the overall optimization procedure.The LLM can generate or modify initialization, kernel functions, acquisition functions, or candidate-search strategies, with predefined interfaces supporting compatibility [11]–.Source: C. Combining LLMs and Bayesian… · pp. 2–3
  • The proposed framework’s stated aim is to connect LLMs, Bayesian optimization, and wireless systems toward self-evolving wireless digital twins.The figure caption identifies these connections but does not specify their visual encoding.Source: Figure 2 · p. 3

D. Towards Self-Evolving Wireless Digital Twins

  • Algorithm-level self-evolution changes selected optimization components according to the task and accumulated experience while retaining the BO workflow.This contrasts with conventional online adaptation of system states, model parameters, or control decisions within a predefined algorithm.Source: D. Towards Self-Evolving Wireless… · p. 3

III. AN LLM-ASSISTED BO FRAMEWORK FOR WIRELESS DIGITAL TWINS

The framework links wireless optimization, accumulated experience, and adaptation of selected BO components in a closed loop. BO retains a modular optimization workflow, while an experience database supplies records that can inform adaptation.

III. AN LLM-ASSISTED BO FRAMEWORK FOR WIRELESS DIGITAL TWINS

  • The four-module framework connects a BO engine, database, prompt builder, and LLM-driven adaptation module in a loop linking optimization, experience accumulation, and component adaptation.Different wireless tasks can arrive over time, and BO returns candidate solutions for evaluation by the physical system.Source: §III · p. 3, A. Bayesian Optimization Engine · p. 3

A. Bayesian Optimization Engine

  • BO iterates through initialization, GP regression, and acquisition-function maximization to model the objective and select new candidates.The GP kernel determines the surrogate covariance structure, while the acquisition function balances predicted performance and uncertainty.Source: A. Bayesian Optimization Engine · p. 3
  • The modular BO workflow allows individual components to be replaced without redesigning the complete optimization procedure.The LLM may return a discovered initialization method, GP kernel, or acquisition function through the component interface.Source: A. Bayesian Optimization Engine · p. 3

B. Experience Database

  • The experience database stores task identity and description, BO code, and observed performance, linking wireless tasks to algorithm implementations and outcomes.Relevant records can be retrieved by task similarity, algorithm structure, or observed performance.Source: B. Experience Database · p. 3
  • The database is updated after new BO components are evaluated, adding accumulated experience for later LLM-based adaptation.Fig. 3 depicts LLM-assisted GP kernel discovery with island-based evolutionary search and BO performance feedback.Source: B. Experience Database · p. 3, Figure 3 · p. 4

C. Prompt Builder

The prompt builder supplies task information and relevant optimization experience to the LLM. The LLM can retain the BO configuration or adapt selected components while leaving the overall BO workflow intact.

C. Prompt Builder

  • The prompt builder combines the current wireless-task description with relevant records retrieved from the experience database.Human or other-agent knowledge and instructions can also be included.Source: C. Prompt Builder · p. 4
  • The resulting prompt gives the LLM task information and optimization experience for adaptation.Source: C. Prompt Builder · p. 4

D. LLM-Driven BO Adaptation

  • The LLM evaluates whether the current BO configuration remains suitable for the new wireless task and can retrieve relevant historical task–algorithm–performance records.Source: D. LLM-Driven BO Adaptation · p. 4
  • If the configuration remains suitable, the LLM retains existing BO tools; otherwise, it identifies a component to modify.Source: D. LLM-Driven BO Adaptation · p. 4
  • The LLM can generate an initialization method, GP kernel, or acquisition function and return it through a predefined interface without redesigning the complete BO procedure.Source: D. LLM-Driven BO Adaptation · p. 4
  • BO performs online adaptation through surrogate updates and candidate selection, while the LLM modifies selected BO components at a slower algorithmic level.Together, the loops retain a stable BO backbone while allowing its optimization mechanism to evolve across changing tasks.Source: D. LLM-Driven BO Adaptation · p. 4

IV. SIMULATION EXPERIMENTS

The simulation is a proof of concept for LLM-assisted BO component adaptation, using GP kernel discovery as its representative case. It holds the overall BO procedure fixed and evolves only the kernel.

IV. SIMULATION EXPERIMENTS

  • The simulation demonstrates feasibility through GP kernel discovery as a representative example of LLM-assisted BO component adaptation.The stated purpose is not to implement every module of the proposed framework.Source: §IV · p. 4
  • Fig. 4 presents the structure of the LLM-discovered GP kernel for the multi-user beam-selection task.Source: Figure 4 · p. 5
  • Fig. 5 presents BO convergence with the LLM-discovered and standard GP kernels on the training tasks.Source: Figure 5 · p. 5
  • The experimental design keeps the overall BO procedure fixed while the LLM evolves only the kernel function.Source: §IV · p. 5

A. Wireless Optimization Task

The study evaluates Gaussian-process kernels on a multi-user beam-selection task and describes an LLM-assisted process for evolving kernels while holding the BO structure fixed. The discovered kernel combines single-user beam similarity with pairwise user interactions.

A. Wireless Optimization Task

  • The task assigns one of 64 DFT-codebook beams to each of 10 users, mapping each configuration to a 20-dimensional GP input and optimizing sum spectral efficiency.Simulated urban channels use an 8 × 8 uniform planar array at 3.5 GHz, with total transmit power divided equally among users.Source: A. Wireless Optimization Task · p. 5
  • Across 50 channel-and-user realizations, 30 tasks support LLM-based kernel discovery and 20 are reserved for testing; each kernel receives 10 shared initial observations and 40 BO iterations.Initialization, GP fitting, and acquisition-function procedures are held identical across kernels; EI is used throughout.Source: A. Wireless Optimization Task · p. 5, B. LLM-Based Kernel Discovery · p. 5

B. LLM-Based Kernel Discovery

  • The discovered kernel combines averaged per-user Matérn-5/2 similarities with multiplicative pairwise Matérn-3/2 similarities, weighted by learned positive values.The single-user component captures similarity in individual beam selections, while the pairwise component reflects user coupling caused by interference.Source: B. LLM-Based Kernel Discovery · p. 5
  • The LLM proposes kernels through local modification, cross-island combination, or global exploration, and BO evaluation feeds performance back into the kernel population.Candidate kernels are maintained in two islands alongside their code, design idea, and observed BO performance.Source: B. LLM-Based Kernel Discovery · p. 5

C. Performance Evaluation

The discovered GP kernel outperforms standard kernels on both training and held-out test tasks, with a larger reported gain on training tasks.

C. Performance Evaluation

  • 19.7%: after 40 BO iterations on 30 training tasks, the discovered kernel improves performance relative to the strongest standard kernel, Matérn-3/2.The discovered kernel reaches a normalized best objective of 70.46%, compared with 58.85% for Matérn-3/2.Source: C. Performance Evaluation · p. 5
  • 8.7%: on 20 test tasks, the discovered kernel achieves a normalized final objective of 0.6482 versus 0.5962 for the strongest standard baseline.Table I compares the discovered kernel with standard kernels; the test tasks were not used during kernel discovery.Source: Table I · p. 6, C. Performance Evaluation · p. 6

V. OPEN CHALLENGES AND RESEARCH DIRECTIONS

The article identifies task changes and reliable validation of generated BO components as challenges to practical, long-term wireless-DT use.

V. OPEN CHALLENGES AND RESEARCH DIRECTIONS

  • Practical, long-term wireless-DT use remains a future challenge for the proposed algorithm-level self-evolution approach.Source: §V · p. 6

A. Adaptation under Task Changes

  • The simulations use tasks from one general system model, leaving suitability under changes to channels, traffic, mobility, network scale, objectives, or constraints unresolved.Moderate task changes may allow reuse of discovered components, whereas larger changes may require adapting initialization, the surrogate model, kernel, or acquisition function.Source: A. Adaptation under Task Changes · p. 6

B. Reliable LLM-Generated BO Components

  • Generated BO components need validation before deployment, and broader components may require checks beyond those used for generated kernels.Suggested checks include interface compatibility, numerical testing, constraint verification, and performance prediction.Source: B. Reliable LLM-Generated BO Components · p. 6

C. Computational Cost and Adaptation Latency

The conclusion reports kernel-discovery gains on training and test tasks, while identifying adaptation cost and latency as unresolved deployment concerns.

C. Computational Cost and Adaptation Latency

  • Algorithm-level adaptation adds computation for processing task and historical information, generating candidates, and evaluating them; slow adaptation may make a component unsuitable by deployment.The concern is acute when network configurations change over short timescales; lightweight strategies must balance optimization improvement with adaptation cost and latency.Source: C. Computational Cost and Adaptation… · p. 6

VI. CONCLUSIONS

  • The discovered kernel improves final BO performance by 19.7% on training tasks and 8.7% on test tasks versus the strongest standard kernel baseline.Source: §VI · p. 6
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