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Constrained Bayesian Optimization for Hierarchical Federated Learning in IoT Networks for Plant Disease Classification

Athanasios Papanikolaou, Athanasios Tziouvaras, Apostolos Xenakis, Periklis Chatzimisios, Shameem A. Puthiya Parambath, George Floros, Enrica Zereik, Ivan Petrovic, Fabio Bonsignorio

arXiv:2609.06830v1cs.LGcs.DC

TL;DR

Resource-constrained IoT HFL must balance predictive performance with energy consumption and execution time, a challenge relevant to agricultural plant-disease classification. The paper uses constrained Bayesian Optimization to configure HFL under deployment-specific trade-offs and constraints. Across 30 independent runs, it explored 11.11% of the search space and every run found a solution within 1% of the exhaustive-search optimum, with a mean relative optimality gap of 0.056%.

  • Problem

    Resource-constrained IoT HFL requires configuration that balances predictive performance against energy consumption and execution time.

    Source: §I · p. 1

  • Method

    The framework uses constrained Bayesian Optimization to select the backbone, aggregation strategy, and communication rounds, with federation size set by spatial coverage and a weighted objective subject to deployment constraints.

    Source: §I · pp. 1–2, A. Search Space and Deployment Model · p. 2

  • Results

    11.11% of the search space was explored, and all runs found solutions within 1% of the exhaustive-search optimum, with a mean relative optimality gap of 0.056%.

    Source: §VI · p. 5, B. Bayesian Optimization Results · p. 5

  • Takeaways & Limitations

    The results indicate the potential of constrained Bayesian Optimization for efficient, resource-aware HFL configuration in smart agricultural IoT environments.

    Source: §VI · p. 5

Abstract

from arXiv · show

The deployment of Hierarchical Federated Learning (HFL) in resource-constrained Internet of Things (IoT) environments requires careful configuration to balance predictive performance with energy consumption and execution time. This challenge is particularly relevant to smart agriculture, where distributed IoT devices can support automated plant disease classification while operating under limited computational and communication resources. This paper presents a constrained Bayesian Optimization framework for the efficient configuration of HFL deployments. The proposed approach jointly explores the deep learning backbone architecture, aggregation strategy, and number of communication rounds, while the federation size is determined according to the spatial coverage requirements of the agricultural deployment. A weighted objective function captures user-defined trade-offs among energy consumption, execution time, and predictive performance, while explicit constraints ensure compliance with deployment-specific resource and accuracy requirements. The framework is evaluated on an IoT-based plant disease classification task considering multiple deep learning architectures, federated aggregation strategies, and communication-round settings. Experimental results across 30 independent optimization runs show that the proposed approach explores only 11.11% of the search space, while consistently identifying solutions within 1% of the exhaustive-search optimum, with a mean optimality gap of only 0.056%.

I. INTRODUCTION

Plant disease classification must be deployed in agricultural IoT settings where resource limits make centralized processing and manual or exhaustive HFL configuration costly. The paper proposes constrained Bayesian Optimization to configure HFL while accounting for deployment requirements.

I. INTRODUCTION

  • Centralized deep-learning pipelines raise practical concerns in resource-constrained IoT networks, while evaluating HFL configurations manually or exhaustively is prohibitively expensive.Configuration choices include backbone architecture, aggregation strategy, communication rounds, and participating-device count.Source: §I · p. 1
  • Federated Learning lets IoT nodes train a shared model without exchanging raw data, but HFL performance is sensitive to configuration choices.Prior agricultural FL work includes crop-disease classification and yield prediction.Source: §I · p. 1
  • The paper formulates HFL configuration as a constrained optimization problem that jointly considers architecture and training parameters under deployment-specific requirements.The framework extends prior work,.Source: §I · pp. 1–2
  • A configurable weighted objective captures user-defined trade-offs among energy, execution time, and predictive performance, while explicit constraints enforce resource and performance requirements.Source: §I · p. 2
  • The framework fixes federation size according to agricultural spatial coverage and uses constrained Bayesian Optimization to select architecture, aggregation strategy, and communication rounds without exhaustive search.It is evaluated on plant-disease classification in a resource-constrained IoT setting, with near-optimal configuration using limited evaluations.Source: §I · p. 2

II. BACKGROUND

The paper defines HFL configuration around device-side learning, model choices, and deployment-specific resource and performance requirements. Farm geometry sets federation size, while architecture, aggregation, and communication rounds form the searched configuration.

A. Federated Learning

  • HFL adds intermediate aggregation layers between participating devices and the global server, bringing aggregation closer to data sources.The paper considers FedAvg, FedProx, and FedAvgM, which respectively average local parameters, limit client drift with proximal regularization, and smooth updates with server-side momentum.Source: A. Federated Learning · p. 2

B. Deep Neural Network Models

  • The architecture search includes EfficientNet-B0, ResNet-50, and MobileNetV3-Large, which provide alternatives with different computational characteristics.Source: B. Deep Neural Network Models · p. 2

III. RESOURCE-AWARE HFL CONFIGURATION PROBLEM

  • The HFL configuration problem balances predictive performance against energy consumption and execution time, with deployment requirements defining feasible configurations.User preferences and explicit constraints govern these objectives; farm spatial coverage determines federation size, while architecture, aggregation, and communication rounds are optimization variables.Source: §III · p. 2

A. Search Space and Deployment Model

  • The configuration search uses backbone, aggregation strategy, and communication-round count; farm geometry determines participating devices before optimization.A coverage-efficiency coefficient accounts for overlap and boundary losses, and the federation-size estimate assumes 80% effective coverage of the ideal circular region; the value can be adjusted for deployment geometry.Source: A. Search Space and Deployment Model · p. 2
  • The energy scaling approximation accounts for federation size and communication rounds, while the execution-time approximation depends only on rounds under assumptions of predominantly parallel client operations and limited coordination overhead.The models extend reference measurements taken at federation size N0 and round count R0.Source: A. Search Space and Deployment Model · pp. 2–3
  • A fitted saturation function approximates round-dependent predictive performance for each model–aggregator pair, but direct measured F1 values are used when available.The experimental search is limited to Rmax = 30 because measured round-level data are available for R = 1, . . . , 30, avoiding extrapolated performance values.Source: A. Search Space and Deployment Model · p. 3

B. Weighted Objective and Constraints

The objective normalizes resource use by user-specified budgets and combines normalized quantities with predictive performance. Explicit limits define which configurations are feasible.

B. Weighted Objective and Constraints

  • Energy consumption and execution time are normalized by their user-specified budgets, while F1-score needs no further scaling because it lies within [0, 1].Normalized energy or time above one indicates that the corresponding budget is exceeded.Source: B. Weighted Objective and Constraints · p. 3
  • The scalar objective combines normalized quantities using user-defined coefficients for energy consumption, execution time, and predictive performance.The coefficients form a valid convex combination.Source: B. Weighted Objective and Constraints · p. 3
  • Explicit constraints impose maximum energy and execution time, minimum predictive performance, and an admissible communication-round range.The objective ranks feasible candidates, while constraints exclude configurations that violate deployment requirements.Source: B. Weighted Objective and Constraints · p. 3

C. Optimization Problem

The configuration problem selects the minimum-objective candidate from the subset satisfying the constraints. Because evaluating a new candidate requires HFL training, the study emulates expensive evaluations using previously collected measurements.

C. Optimization Problem

  • The selected configuration is the one that minimizes scalar objective L(x) over the feasible set Ω.Ω is the subset of configurations satisfying the constraints.Source: C. Optimization Problem · p. 3
  • Evaluating an untested configuration requires running its HFL training process and obtaining predictive and resource measurements.This makes configuration selection an expensive black-box optimization task.Source: C. Optimization Problem · p. 3
  • Previously collected round-level measurements emulate expensive evaluations, enabling controlled assessment against the optimum from the complete discrete search space.Source: C. Optimization Problem · p. 3

IV. CONSTRAINED BAYESIAN OPTIMIZATION

Because evaluating an untested HFL configuration can require training and measuring it, the paper uses Bayesian Optimization to search for promising feasible configurations with fewer evaluations. It models objective quality and constraint satisfaction separately and combines them in a constrained acquisition function.

IV. CONSTRAINED BAYESIAN OPTIMIZATION

  • Bayesian Optimization guides the search toward promising feasible configurations while limiting expensive evaluations.Each untested configuration may require HFL training and collection of predictive and resource-related measurements.Source: §IV · p. 3
  • A Gaussian Process regression model approximates the scalar objective, while a separate probabilistic model estimates constraint satisfaction.Source: §IV · pp. 3–4
  • The constrained acquisition function favors candidates expected to improve the best feasible solution while maintaining a high probability of feasibility.Source: §IV · p. 4

A. Surrogate Models and Candidate Encoding

The surrogate models represent each configuration numerically and estimate both its objective and its likelihood of meeting deployment constraints. The encoding distinguishes categorical architecture and aggregation choices from the communication-round variable.

A. Surrogate Models and Candidate Encoding

  • The backbone model and aggregation strategy are one-hot encoded, while the communication-round value is normalized to [0, 1].The configuration is represented as x = (m, a, R), with one-hot vectors for the selected model and aggregation strategy.Source: A. Surrogate Models and Candidate… · p. 4
  • A Gaussian Process regression model fitted to evaluated configurations predicts the objective's mean and standard deviation for each unevaluated candidate.The objective surrogate uses a Matérn kernel.Source: A. Surrogate Models and Candidate… · p. 4
  • A separate Gaussian Process classifier uses feasible/infeasible labels to estimate the probability of satisfying energy, execution-time, and predictive-performance requirements.Source: A. Surrogate Models and Candidate… · p. 4

B. Acquisition and Search Procedure

The search starts with unique random configurations and then selects new candidates using Expected Improvement weighted by estimated feasibility. If no feasible candidate has yet been found, selection initially prioritizes the probability of feasibility.

B. Acquisition and Search Procedure

  • When no feasible configuration has been observed, candidate selection prioritizes estimated feasibility until one is identified.The process begins with a small set of unique randomly selected configurations.Source: B. Acquisition and Search Procedure · p. 4
  • Expected Improvement measures the expected reduction relative to the best feasible objective observed at iteration t.For minimization, its expression uses the standard normal cumulative and probability density functions; ξ controls the exploration–exploitation trade-off.Source: B. Acquisition and Search Procedure · p. 4
  • The acquisition function weights Expected Improvement by estimated feasibility and selects the next candidate from configurations not yet tested.Source: B. Acquisition and Search Procedure · p. 4
  • The study uses six unique initialization configurations and a 30-evaluation budget, evaluating each selected candidate once before updating both probabilistic models.Source: B. Acquisition and Search Procedure · p. 4

V. EXPERIMENTAL EVALUATION

The optimization setup fixes the federation size using an assumed farm deployment and searches model–aggregator combinations across communication-round settings. The reported feasible optimum is EfficientNet-B0 with FedAvg at four rounds, with ResNet-50 and FedProx at two rounds as the close second-best configuration.

A. Optimization Setup and Ground-Truth Benchmark

B. Bayesian Optimization Results

Across 30 independent runs, constrained Bayesian Optimization consistently found feasible solutions close to the exhaustive-search optimum. The search approached that optimum early and identified each run’s final best solution after a small fraction of the configuration space had been explored.

B. Bayesian Optimization Results

  • Each of the 30 runs started from six unique randomly selected configurations and had a budget of 30 evaluations.Source: B. Bayesian Optimization Results · p. 5
  • 0.056% mean relative optimality gap; all runs ended within 1% of the exhaustive-search optimum, and 63.33% recovered it exactly.A feasible solution was identified in every run; the median gap was 0% and the maximum was 0.152%.Source: Table I · p. 5, B. Bayesian Optimization Results · p. 5
  • After 15 evaluations (5.56% of the search space), the median optimality gap was 0.152%, and 56.67% of runs were within 1% of the optimum; that proportion reached 100% by 30 evaluations.The proportion within 1% was 80.00% after 20 evaluations and 86.67% after 25.Source: B. Bayesian Optimization Results · p. 5
  • The final best solution in each run was first identified at a median iteration of 15.5, approximately 5.74% of the complete search space.The authors report that the procedure concentrates search near the globally optimal region while requiring only a small fraction of exhaustive evaluations.Source: B. Bayesian Optimization Results · p. 5

VI. CONCLUSIONS

The paper presents constrained Bayesian Optimization for configuring HFL in resource-constrained IoT plant-disease classification. Across its experiments, it explores 11.11% of the search space while finding solutions within 1% of the exhaustive-search optimum in every run.

VI. CONCLUSIONS

  • The framework targets efficient HFL configuration for plant disease classification in resource-constrained IoT environments.Source: §VI · p. 5
  • It jointly optimizes the learning architecture, aggregation strategy, and communication rounds under energy, execution-time, and predictive-performance constraints.Source: §VI · p. 5
  • 11.11% of the search space was explored, and every run found a solution within 1% of the exhaustive-search optimum.Source: §VI · p. 5

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