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Fractional Order Federated Learning for Battery Electric Vehicle Energy Consumption Modeling

Mohammad Partohaghighi, Roummel Marcia, Bruce J. West, YangQuan Chen

TL;DR

Experiments on two real-world BEV energy prediction datasets show that FO-RI-FedAvg achieves improved accuracy and more stable convergence compared to strong federated baselines, particularly under reduced client participation.

Abstract

Federated learning on connected electric vehicles (BEVs) faces severe instability due to intermittent connectivity, time-varying client participation, and pronounced client-to-client variation induced by diverse operating conditions. Conventional FedAvg and many advanced methods can suffer from excessive drift and degraded convergence under these realistic constraints. This work introduces Fractional-Order Roughness-Informed Federated Averaging (FO-RI-FedAvg), a lightweight and modular extension of FedAvg that improves stability through two complementary client-side mechanisms: (i) adaptive roughness-informed proximal regularization, which dynamically tunes the pull toward the global model based on local loss-landscape roughness, and (ii) non-integer-order local optimization, which incorporates short-term memory to smooth conflicting update directions. The approach preserves standard FedAvg server aggregation, adds only element-wise operations with amortizable overhead, and allows independent toggling of each component. Experiments on two real-world BEV energy prediction datasets, VED and its extended version eVED, show that FO-RI-FedAvg achieves improved accuracy and more stable convergence compared to strong federated baselines, particularly under reduced client participation.

Fractional Order Federated Learning for Battery Electric Vehicle Energy Consumption Modeling

TL;DR

Experiments on two real-world BEV energy prediction datasets show that FO-RI-FedAvg achieves improved accuracy and more stable convergence compared to strong federated baselines, particularly under reduced client participation.

Abstract

Federated learning on connected electric vehicles (BEVs) faces severe instability due to intermittent connectivity, time-varying client participation, and pronounced client-to-client variation induced by diverse operating conditions. Conventional FedAvg and many advanced methods can suffer from excessive drift and degraded convergence under these realistic constraints. This work introduces Fractional-Order Roughness-Informed Federated Averaging (FO-RI-FedAvg), a lightweight and modular extension of FedAvg that improves stability through two complementary client-side mechanisms: (i) adaptive roughness-informed proximal regularization, which dynamically tunes the pull toward the global model based on local loss-landscape roughness, and (ii) non-integer-order local optimization, which incorporates short-term memory to smooth conflicting update directions. The approach preserves standard FedAvg server aggregation, adds only element-wise operations with amortizable overhead, and allows independent toggling of each component. Experiments on two real-world BEV energy prediction datasets, VED and its extended version eVED, show that FO-RI-FedAvg achieves improved accuracy and more stable convergence compared to strong federated baselines, particularly under reduced client participation.
Paper Structure (179 sections, 49 equations, 25 figures, 34 tables, 1 algorithm)

This paper contains 179 sections, 49 equations, 25 figures, 34 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Integer-order vs. non-integer-order FL (terminology).
  3. Contributions.
  4. Organization.
  5. Methodology
  6. Federated learning setup and notation
  7. Local and global objectives.
  8. Communication rounds and partial participation.
  9. Client variability model.
  10. Fractional-order local update dynamics
  11. Motivation and scope.
  12. Local update notation.
  13. Standard local SGD (baseline).
  14. Fractional-order local SGD (FO-SGD): Caputo-inspired surrogate.
  15. Restriction to $n=1$ (i.e., $0<\alpha\le 1$).
  16. ...and 164 more sections

Figures (25)

  • Figure 1: Pipeline of FO-RI-FedAvg (Fractional-Order Roughness-Informed Federated Averaging).
  • Figure 2: Test RMSE vs. rounds on VED dataeset .
  • Figure 3: Test RMSE vs. rounds on eVED dataeset .
  • Figure 4: Anytime performance on VED using best-so-far RMSE versus rounds.
  • Figure 5: Anytime performance on eVED using best-so-far RMSE versus rounds .
  • ...and 20 more figures