EH-FedSAG: Variance-Reduced Federated Learning with Energy-Aware Participation in Energy-Harvesting IoT

Technical Summary of "EH-FedSAG: Variance-Reduced Federated Learning with Energy-Aware Participation in Energy-Harvesting IoT"

Problem Statement
Federated Learning (FL) in Energy-Harvesting (EH) networks faces significant challenges due to the intermittent and stochastic nature of energy arrivals. Unlike conventional edge devices with stable power, EH devices rely on environmental energy sources, leading to time-varying energy availability. This introduces a dual layer of randomness:

1. Unstable Participation: Devices may lack sufficient energy for local computation or uplink transmission in a given round, leading to a stochastic subset of participating devices.
2. Convergence Instability: In standard FL algorithms like FedAvg, partial participation introduces variability in aggregated updates, often resulting in a non-vanishing error floor and unstable convergence behavior. This issue is exacerbated in EH systems where energy constraints further limit the consistency of device participation.

While prior works have addressed energy-aware device selection and efficient protocols, the combined impact of EH constraints, energy-aware participation, and server-side memory-based variance reduction has not been studied within a unified framework.

Methodology: EH-FedSAG
The paper proposes EH-FedSAG, a server-memory-based variance-reduced FL method adapted for EH environments. The system operates under a slot-based EH model where:

• Energy Dynamics: Devices follow a "harvest-store-use" paradigm with finite battery capacity. Energy arrivals are modeled as i.i.d. Bernoulli processes.
• Feasibility Constraints: A device can only participate if its battery level at a specific starting slot ($s^*$) is sufficient to cover both local training ($\Omega$ slots) and transmission (1 slot).
• Device Selection: The server employs an age-based selection policy. Among devices with sufficient energy, those that have not been selected recently (higher "selection age") are prioritized to ensure long-term fairness. A maximum of $M$ devices can be scheduled per round due to orthogonal channel limitations.

Algorithmic Core:
EH-FedSAG integrates the SAGA (Stochastic Average Gradient Algorithm) principle into the EH-FL protocol:

1. Local Update: Selected devices perform $B$ steps of local Stochastic Gradient Descent (SGD) and transmit the model difference $\delta_t^{(k)} = w_t - w_{t,B}^{(k)}$.
2. Server Memory: The server maintains a memory vector $m_t^{(k)}$ for each device $k$, storing the most recently received update.
3. Variance Reduction: Instead of a simple average, the server computes a variance-reduced direction $v_t$ by combining the mean of all stored memories with the fresh updates from currently active devices:
   $$v_t = \bar{m}_t + \frac{1}{|P_t|} \sum_{k \in P_t} (\delta_t^{(k)} - m_t^{(k)})$$
   where $\bar{m}_t$ is the mean of all stored memories.
4. Global Update: The global model is updated using this reduced-variance direction. If no devices participate, the model remains unchanged.

Key Contributions

1. Unified Framework: The authors propose an energy-aware EH-FL framework that explicitly models slot-level battery dynamics, enforces per-round participation constraints based on energy feasibility, and employs an age-based device selection mechanism.
2. Algorithm Development: They develop EH-FedSAG, a memory-based variant of EH-FedAvg that leverages server-side memory to mitigate variance caused by time-varying device availability and partial participation.
3. Empirical Characterization: The paper characterizes the relationship between test accuracy and training rounds under varying energy arrival probabilities ($P_h$) and data heterogeneity (controlled by Dirichlet parameter $\alpha$) across two network architectures (SmallCNN and SmallResNet).

Experimental Results
The proposed method was evaluated against a vanilla EH-FedAvg baseline using CIFAR-10 image classification with $K=100$ devices and $M=25$ channels over 1,000 rounds.

• Performance under Scarce Energy: Under low energy arrival probabilities ($P_h = 0.02$), EH-FedAvg exhibited significant oscillations. EH-FedSAG achieved approximately 3% higher test accuracy and demonstrated greater robustness to participation-induced fluctuations.
• Variance Reduction: EH-FedSAG consistently achieved substantially lower late-stage accuracy variance compared to EH-FedAvg. For instance, at $P_h = 0.06$, the variance was reduced from 0.9401 (FedAvg) to 0.0421 (FedSAG).
• Convergence Speed: EH-FedSAG reached a stable 50% test accuracy threshold approximately 26% faster than EH-FedAvg in the $P_h = 0.06$ scenario.
• Non-I.I.D. Data: Under heterogeneous data distributions (low $\alpha$), EH-FedAvg suffered from sharp accuracy drops due to the unrepresentative nature of the active subset. EH-FedSAG maintained a smoother trajectory by leveraging stored information from previously active devices, effectively decoupling the global update from the instantaneous set of active devices.

Significance and Claims
The paper claims that incorporating server-side variance reduction into EH-FL is an effective strategy for enhancing training stability. The primary advantage of EH-FedSAG is most pronounced when energy availability is scarce and data distributions are non-independent and identically distributed (non-i.i.d.). By compensating for missing updates from unavailable devices using stored memories, the algorithm produces more consistent and predictable model performance across communication rounds. This is particularly beneficial for low-power IoT deployments where intermittent participation and limited communication budgets make early stopping and stable performance highly desirable.

The authors note that future work could extend this framework to unreliable wireless links, theoretical convergence analysis under EH constraints, and systems with computationally heterogeneous devices.