Energy-Efficient Federated Learning

Updated 23 November 2025

Energy-efficient federated learning is a distributed training approach that minimizes energy consumption via joint optimization of communication and computation while ensuring privacy and fairness.
It employs advanced methods like dual decomposition, alternating optimization, and convex reformulation to address non-convex resource allocation and heterogeneous device challenges.
Experimental validations show energy savings up to 90% with maintained accuracy, making it viable for IoT, UAV, AIoT, and renewable-powered deployments.

Energy-efficient federated learning (EEFL) involves algorithmic and systems-level strategies designed to minimize the total energy consumption of distributed training—encompassing both wireless communication and local computation—while maintaining privacy, accuracy, and participation fairness among heterogeneous edge devices. EEFL has seen rapid maturation through rigorous formalization of the resource allocation problem, design of decomposable optimization and learning frameworks, and empirical validation across wireless, IoT, AIoT, UAV, and renewable-aware deployments. The field increasingly intersects device scheduling, communication-compression co-design, hardware-aware model adaptation, and green-AI/carbon-aware systems.

1. Fundamental Problem Formulation

Most EEFL frameworks cast the design objective as constrained optimization over per-round participant selection, communication resource allocation, and model compression. For wireless edge systems, one prototypical formulation arises in the FairEnergy framework (Marnissi et al., 19 Nov 2025), which, for $N$ clients in round $r$ , seeks binary vector $\{x_i\}$ for selection, bandwidth vector $\{b_i\}$ , and compression ratios $\{c_i\}$ that minimize total energy: $\min_{\{x_i,b_i,c_i\}} \sum_{i=1}^N x_i\,E_i(b_i, c_i)$ with $E_i(b_i, c_i)$ the communication energy per client, subject to sum-bandwidth $\sum_{i=1}^N x_i\,b_i \le B_\mathrm{tot}$ , compression $c_\mathrm{min}\le c_i \le 1$ , EMAs for fairness $q_i^r \ge \tau_\mathrm{min}$ , and $x_i\in\{0,1\}$ . The communication rate is modeled via the Shannon formula, and fairness uses a per-client exponentially weighted moving average.

Several other frameworks generalize this with per-round computation energy, constraints on convergence accuracy, latency, device memory, or total carbon emissions (Compaoré et al., 16 Sep 2025, Kumar et al., 23 Nov 2024, Khowaja et al., 2022). Common variables include CPU frequency, transmission power, quantization depth, and model-rate (fraction of active weights).

2. Resource Allocation and Decomposition Techniques

To address the mixed-integer, non-convexity in such formulations, advanced methods decompose problem structure, relax discrete variables, and apply dual decomposition or convexification:

Dual relaxation and primal-dual decomposition: Variables such as participation $x_i$ are relaxed to continuous intervals, leading to closed-form threshold rules for device selection. Lagrangian multipliers enforce bandwidth and fairness constraints (Marnissi et al., 19 Nov 2025).
Per-device subproblem separation: The partial Lagrangian splits into per-client channels, allowing parallel optimization via, e.g., golden-section search for single-variable minimization (compression/bandwidth) (Marnissi et al., 19 Nov 2025).
Alternating optimization and SCA: For joint UAV trajectory, user participation, power/data allocation in aerial FL, successive convex approximation and block-coordinate alternating optimization convexify constraints, enabling practical solution of the overall joint energy model (Fu et al., 5 Aug 2025).
Convex reformulation: Many EEFL models exploit change-of-variable and polymatroid capacity region arguments (especially for NOMA or MACs) to yield convex subproblems for bandwidth/power updates (Mo et al., 2020).
Iterative greedy or heuristic clustering: AIoT-centric EEFL employs offline clustering (label- or diversity-based) and greedy cluster assignment for energy-stable participant selection (Pereira et al., 14 May 2025).

These decomposition and approximation methods ensure scalable, robust convergence under non-convex resource constraints, making them ideal for large-scale wireless deployments.

3. Model Compression, Quantization, and Data Augmentation

Model update compression is central to energy proportionality, with compression ratio $c_i$ and quantization depth $n$ directly impacting transmission energy, computation cycles, and convergence variance:

Stochastic quantization and rounding: Updates are quantized to $n$ bits, with unbiased stochastic rounding to minimize quantization error. The variance scales inversely with $2^{2(n-1)}$ (Compaoré et al., 16 Sep 2025, Chen et al., 2020).
Gradient sparsification, pruning: Only the largest-magnitude updates are transmitted or a fraction $\rho$ of model weights are zeroed out, cutting per-iteration compute and communication (Hou et al., 3 Aug 2025, Shi et al., 2021).
Diffusion-based data augmentation: Synthetic local data patches, generated via learned diffusion models, mitigate non-IID-induced slow convergence but introduce a direct generation energy cost (Hou et al., 3 Aug 2025). Optimal data augmentation balances increased convergence rate against augmentation overhead.
Ordered dropout and flexible masking: For carbon-aware adaptation, partial model broadcast based on per-domain energy forecasts and batch capacity reduces energy and carbon per round while preserving aggregation compatibility (Kumar et al., 23 Nov 2024).

Model adaptation, ordered dropout, and compressed aggregation are contributing to practical scaling of EEFL in heterogeneous and resource-constrained networks.

4. Scheduling, Fairness, and Participation Optimization

Energy minimization must not sacrifice client participation regularity or cohort fairness—often formalized via long-term selection EMAs, adaptive dual weights, and clustering:

Contribution-based selection: Clients are ranked or weighted based on compressed update magnitude, promoting selection of those whose updates are minimally compressed but significant in value (Marnissi et al., 19 Nov 2025).
EMA-based fairness and min-rate constraints: Each client's selection history is recursively tracked; enforced thresholds guarantee minimal participation rates (Marnissi et al., 19 Nov 2025). The fairness penalty in the objective tunes energy vs. fairness.
Clustering for heterogeneity mitigation: AIoT schemes leverage offline clustering by label or diversity, increasing convergence speed and lowering training/communication energy by avoiding per-round global ranking (Pereira et al., 14 May 2025).
DRL and RL-based orchestration: Deep RL agents (notably soft actor-critic) are increasingly adopted to orchestrate compute and communication resource allocation while satisfying hard constraints on battery, latency, and accuracy (Koursioumpas et al., 2023, Kim et al., 2021). Reward shaping includes explicit energy penalties for constraint violation or wasted transmissions.

The intersection of selection theory, RL, and clustering methods is advancing state-of-the-art in both fairness and energy regularization.

5. Protocols for Communication, Computation, and Network Control

EEFL typically coordinates multiple protocol layers:

Uplink communication: Protocols range from orthogonal channels (TDMA, FDMA) to non-orthogonal (NOMA) and over-the-air aggregation. NOMA approaches exploit MAC polymatroid structure for improved energy-delay trade-off (Mo et al., 2020, Li et al., 2022).
Dynamic power control and blocklength adaptation: Transmission power is tuned per device and round, often subject to finite blocklength limitations, target packet drop $q$ , and error-aware aggregation (Compaoré et al., 16 Sep 2025).
Network-level architectures: UAV-based parameter servers and relay-assisted protocols optimize flight trajectory, user grouping (single-hop/two-hop/relay), and per-device allocation for minimal overall system energy under latency constraints (Fu et al., 5 Aug 2025, Hashempour et al., 27 Apr 2024).
Multi-tier federation: Distributed clustering, relay selection, and fog-cloud integration reduce long-haul transmission energy by offloading aggregation to cluster heads, suited for ultra-dense or 6G scenarios (Khowaja et al., 2022, Al-Abiad et al., 2021).

Joint design of the communication and computation stack is key to minimizing energy in FL over resource-limited, unreliable, or multi-hop networks.

6. Experimental Validation and Comparative Performance

EEFL studies report substantial savings over classical and non-compression baselines:

Framework	Domain	Energy Saving vs. Baseline	Accuracy Impact	Fairness / Participation
FairEnergy (Marnissi et al., 19 Nov 2025)	Wireless	Up to 79%	Matches greedy	Std. selection ≈ 2.85
ECO (Fu et al., 5 Aug 2025)	UAV	20–50%	Fewer rounds	Slot-level min participation
Quantized FL (Compaoré et al., 16 Sep 2025)	IoT	≈75% (FP8)	≤10% time overhead	Power/latency-optimal
Clustering-AIoT (Pereira et al., 14 May 2025)	AIoT	20–40%	No loss	Stable per-cluster sampling
RL-Orchestration (Koursioumpas et al., 2023)	Wireless	Up to 94%	×3 longer rounds	Penalty zero-violation

In multi-modal, multi-tier, or factory relay scenarios, two-hop relaying and clustering further double energy savings or improve outage rates by 30% compared to single-hop approaches (Hashempour et al., 27 Apr 2024, Khowaja et al., 2022). DRL scheduling and RL-based client selection deliver order-of-magnitude cluster-wide energy reductions in scenarios with stochastic device performance (Koursioumpas et al., 2023, Kim et al., 2021).

7. Trade-offs, Guidelines, and Open Directions

There are explicit trade-offs in EEFL: heavier compression, quantization, or pruning can degrade statistical accuracy or slow convergence; aggressive participation enforcement may boost energy; relay/multi-hop or global data augmentation introduce control overhead. Algorithmic guidelines and practical recommendations include:

Compression ratio: Tune $c_i$ and $n$ to minimize energy while bounding accuracy loss; moderate FP8 quantization offers optimal trade-off in IoT FL (Compaoré et al., 16 Sep 2025).
Participant selection: Use contribution scores and long-term fairness memos to balance energy, accuracy, and fairness (Marnissi et al., 19 Nov 2025).
Clustering: Prefer offline clustering for statistically diverse environments; adjust cluster size to match client heterogeneity and desired energy profile (Pereira et al., 14 May 2025).
Power and CPU allocation: Jointly optimize transmit power and CPU frequency for local rounds, exploiting DVFS and per-device schedules (Mo et al., 2020, Al-Abiad et al., 2021).
Carbon/energy awareness: Employ per-domain model-rate adaptation and ordered dropout for large-scale, renewable-powered deployments (Kumar et al., 23 Nov 2024).
Relay selection: Implement device grouping and relay scheduling via provably optimal algorithms (e.g., SPCA), particularly in factory/industrial settings (Hashempour et al., 27 Apr 2024).
Safe RL orchestration: Integrate explicit energy penalties and constraint-aware rewards in RL-based FL environments to maximize savings with minimal violations (Koursioumpas et al., 2023).

Open directions include fully asynchronous, personalized aggregation compatible with heterogeneous model structures, privacy-preserving energy-efficient protocols, co-optimization of energy-delay-privacy, and continual learning under dynamic device availability and renewable energy supply.

EEFL has rapidly evolved from transmission/computation co-design to joint scheduling-compression-fairness optimization, with methods validated across realistic wireless and edge networks. The field is now moving toward scalable, RL-augmented, carbon-constrained, and heterogeneous-aware FL deployments. Recent results suggest that multi-factor resource allocation, hardware-aware compression, clustering-driven selection, and DRL orchestration can cut energy costs by 40–90% while sustaining fair participation and high statistical accuracy (Marnissi et al., 19 Nov 2025, Fu et al., 5 Aug 2025, Pereira et al., 14 May 2025, Koursioumpas et al., 2023, Kumar et al., 23 Nov 2024).