Fed-Cyclic: Cyclic Federated Learning Variants

• Fed-Cyclic is an umbrella term for cyclic federated learning schemes that use repeated, ordered client or group participation for model updates.
• It encompasses methods such as server-side cyclic aggregation, sequential model passing, and energy-aware cyclic scheduling to improve convergence, stability, or resource utilization.
• Empirical studies show that cyclic designs can reduce communication rounds and boost accuracy in non-i.i.d. data settings and resource-constrained environments.

Searching arXiv for recent and foundational papers on cyclic federated learning variants. arxiv_search: "federated learning cyclic participation cyclic aggregation CyclicFL FedBacys FedCluster serial federated learning" [arxiv_search query="federated learning cyclic participation cyclic aggregation CyclicFL FedBacys FedCluster serial federated learning" max_results=10] “Fed-Cyclic” is best understood as an umbrella term for federated learning schemes in which participation, aggregation, or model transfer follows a repeated ordered cycle rather than i.i.d. client sampling. In the arXiv literature, the term is mostly informal rather than the name of a single canonical algorithm. It encompasses at least six distinct constructions: server-side cyclic aggregation, cyclic client-side pre-training, FedAvg with cyclic client participation, cluster-cycling, serial client-to-client weight transfer, and battery-aware cyclic scheduling for energy-harvesting federated learning (Lee et al., 2022, Zhang et al., 2023, Cho et al., 2023, Chen et al., 2020, Song et al., 2024, Jeong et al., 16 Apr 2025). The common thread is periodic structure over clients or groups; the principal differences are the unit of cyclicity, the location of the cyclic mechanism in the training stack, and the assumptions under which such cyclicity improves convergence, stability, or resource efficiency.

1. Terminology and taxonomy

In the surveyed literature, “Fed-Cyclic” does not denote one standardized protocol. A more precise reading is “cyclic federated learning,” namely FL in which the training process traverses an ordered set of clients or groups, or applies a periodic control law at the server.

Approach	Cyclic unit	Primary role
Cyclic aggregation (Lee et al., 2022)	Server learning rate	Plug-in server-side aggregation modifier
CyclicFL (Zhang et al., 2023)	Ordered clients in pre-training	Cyclic initialization before ordinary FL
CyCP (Cho et al., 2023)	Availability groups	FedAvg with cyclic client participation
FedCluster (Chen et al., 2020)	Clusters	Sequential cluster-wise meta-updates
CWT/CWC (Song et al., 2024)	Individual clients	Serial client-to-client model passing
FedBacys / FedBacys-Odd (Jeong et al., 16 Apr 2025, Jeong et al., 14 Nov 2025)	Battery-aware groups	EHFL scheduling and staged aggregation

Two misconceptions recur. First, cyclic FL is not necessarily strict per-client round robin. FedBacys, for example, is cyclic at the group level and conditional at the client level, because actual participation depends on battery state and timing constraints (Jeong et al., 16 Apr 2025). Second, cyclic FL is not necessarily an end-to-end replacement for FedAvg. CyclicFL uses cyclic traversal only in a pre-training stage and then switches to a conventional FL method such as FedAvg, FedProx, SCAFFOLD, or MOON (Zhang et al., 2023).

2. Structural forms of cyclicity

Most cyclic FL papers begin from the standard federated objective

$$\min_{\theta \in \Theta} F(\theta) \triangleq \frac{1}{N}\sum_{n=1}^{N} F_n(\theta),$$

or an equivalent client-averaged form over local losses (Lee et al., 2022, Cho et al., 2023). What changes is not the objective but the temporal structure by which model updates are produced and composed.

One form is a purely server-side periodic control law. In cyclic aggregation, clients perform their usual local optimization, while the server replaces a fixed aggregation coefficient with a cyclic server learning rate,

$$\theta_{i_g+1} \leftarrow \gamma_{\text{cyclic}(i_g)} \cdot ServerOpt(\{\theta_{i_g}^m\}_{m=1}^{M}),$$

where $\gamma_{\text{cyclic}(i_g)}$ oscillates around a baseline fixed rate and is applied as a plug-in wrapper to FedAvg, FedProx, MOON, or FedRS (Lee et al., 2022). Here cyclicity does not reorder clients; it modulates server update aggressiveness across rounds.

A second form is sequential model passing. In CyclicFL, a randomly initialized model is sent through an ordered subset of clients during a pre-training stage; the output of one client becomes the input to the next, and the final pretrained model is then used to initialize downstream FL (Zhang et al., 2023). FedCluster generalizes the same idea to clusters: one learning round contains multiple cycles of meta-update, with the server aggregating after each cluster and then forwarding the refreshed model to the next cluster (Chen et al., 2020). Serial FL with cyclical weight transfer uses the same client-to-client topology without parallel averaging, so the training trajectory is path-dependent and the client order becomes algorithmically central (Song et al., 2024).

A third form is cyclic scheduling under structured availability. In CyCP, the $M$ clients are partitioned into $\bar M$ groups $\sigma(1),\dots,\sigma(\bar M)$, and at round $(k,i)$ the server can only sample clients from the currently available group $\sigma(i)$ (Cho et al., 2023). FedBacys adds a stricter resource model tailored to energy-harvesting FL. Time is divided into slots and epochs; clients are partitioned into $G$ groups; each group is allocated a group-round of length $R=\lfloor S/G \rfloor$; and local training is launched only when it can finish inside the client’s designated upload window: $$\theta_{i_g+1} \leftarrow \gamma_{\text{cyclic}(i_g)} \cdot ServerOpt(\{\theta_{i_g}^m\}_{m=1}^{M}),$$0 This “train just before transmission” rule couples the cyclic schedule to battery feasibility and update freshness (Jeong et al., 16 Apr 2025).

3. Representative method families

Cyclic pre-training is exemplified by CyclicFL. Its architecture has two stages: P1 is cyclic pre-training on selected AIoT devices, and P2 is ordinary FL fine-tuning initialized from the pretrained model $$\theta_{i_g+1} \leftarrow \gamma_{\text{cyclic}(i_g)} \cdot ServerOpt(\{\theta_{i_g}^m\}_{m=1}^{M}),$$1 rather than a random model (Zhang et al., 2023). The P1 stage samples $$\theta_{i_g+1} \leftarrow \gamma_{\text{cyclic}(i_g)} \cdot ServerOpt(\{\theta_{i_g}^m\}_{m=1}^{M}),$$2 clients per round, visits them sequentially, and avoids public proxy data. The paper’s theory emphasizes two points: sequential SGD over related client tasks can approximate stronger continual-learning procedures when task similarity is high, and pre-training helps most when pre-training and downstream FL data are consistent. CyclicFL is therefore a cyclic FL method in mechanism, but only for initialization.

Cyclic participation in the strict FedAvg sense is formalized by CyCP. The defining feature is that client availability is periodic rather than uniformly random: the server samples $$\theta_{i_g+1} \leftarrow \gamma_{\text{cyclic}(i_g)} \cdot ServerOpt(\{\theta_{i_g}^m\}_{m=1}^{M}),$$3 clients uniformly without replacement from the currently available group, and a full cycle-epoch traverses all groups once in a fixed order (Cho et al., 2023). The analysis introduces separate heterogeneity constants for within-group and across-group mismatch, denoted $$\theta_{i_g+1} \leftarrow \gamma_{\text{cyclic}(i_g)} \cdot ServerOpt(\{\theta_{i_g}^m\}_{m=1}^{M}),$$4 and $$\theta_{i_g+1} \leftarrow \gamma_{\text{cyclic}(i_g)} \cdot ServerOpt(\{\theta_{i_g}^m\}_{m=1}^{M}),$$5, reflecting the fact that cyclic schedules naturally separate intra-group and inter-group heterogeneity.

Cluster-cycling is developed in FedCluster. Devices are partitioned into $$\theta_{i_g+1} \leftarrow \gamma_{\text{cyclic}(i_g)} \cdot ServerOpt(\{\theta_{i_g}^m\}_{m=1}^{M}),$$6 clusters $$\theta_{i_g+1} \leftarrow \gamma_{\text{cyclic}(i_g)} \cdot ServerOpt(\{\theta_{i_g}^m\}_{m=1}^{M}),$$7, and each learning round contains $$\theta_{i_g+1} \leftarrow \gamma_{\text{cyclic}(i_g)} \cdot ServerOpt(\{\theta_{i_g}^m\}_{m=1}^{M}),$$8 inner cycles, one per cluster (Chen et al., 2020). In cycle $$\theta_{i_g+1} \leftarrow \gamma_{\text{cyclic}(i_g)} \cdot ServerOpt(\{\theta_{i_g}^m\}_{m=1}^{M}),$$9, the active cluster performs a FedAvg-style local training step, the cloud aggregates immediately to obtain $\gamma_{\text{cyclic}(i_g)}$0, and the next cluster starts from that updated model. This is a hierarchical cyclic design: parallel averaging within the active cluster, sequential progression across clusters.

Serial client-cycling appears most clearly in cyclical weight transfer and its regularized variant Cyclical Weight Consolidation. In this topology, a single model is passed through clients $\gamma_{\text{cyclic}(i_g)}$1 and then revisits client $\gamma_{\text{cyclic}(i_g)}$2 in the next communication round (Song et al., 2024). CWC augments local optimization with a consolidation term

$\gamma_{\text{cyclic}(i_g)}$3

where $\gamma_{\text{cyclic}(i_g)}$4 is a parameter-wise consolidation matrix accumulated along the cycle and decayed across rounds. This explicitly targets catastrophic forgetting in serial FL.

Battery-aware cyclic scheduling is represented by FedBacys and its selective-participation extension FedBacys-Odd. FedBacys studies EHFL with stochastic charging, local training cost $\gamma_{\text{cyclic}(i_g)}$5, and slot-level actions of transmit, local training, or idle (Jeong et al., 16 Apr 2025). Clients are clustered into groups, intra-group updates are aggregated at temporary hubs, and the intermediate model is passed from one group to the next. FedBacys-Odd adds a selective rule: when the usual three training conditions are satisfied, the client trains only on odd-numbered eligible opportunities, thereby reducing local computation without changing the group-cyclic skeleton (Jeong et al., 14 Nov 2025).

4. Theoretical foundations and convergence results

The theoretical maturity of cyclic FL is uneven across subfamilies. The strongest explicit FedAvg-style convergence results are in the CyCP analysis, which studies local GD, local SGD, and local shuffled SGD under smoothness and a global Polyak–Łojasiewicz condition (Cho et al., 2023). Its main conclusion is that one full cycle behaves like a large gradient step plus structured error terms. For local GD and local SSGD, the asymptotic rate can improve to $\gamma_{\text{cyclic}(i_g)}$6 when the dominant within-group term vanishes, most cleanly when the server selects all clients in the currently available group, $\gamma_{\text{cyclic}(i_g)}$7, or when within-group heterogeneity $\gamma_{\text{cyclic}(i_g)}$8 is negligible. For local SGD, a stochastic variance term remains, so the rate generally stays $\gamma_{\text{cyclic}(i_g)}$9.

FedCluster provides a separate convergence route for nonconvex optimization with local SGD and full participation in the active cluster (Chen et al., 2020). Its bound is expressed through cluster-level heterogeneity

$M$0

and yields

$M$1

Relative to the standard FedAvg nonconvex rate $M$2, the cluster-cycling design improves the round dependence by a factor of $M$3, while also replacing device-level heterogeneity by cluster-level heterogeneity in the error constant.

The most developed EHFL-specific theory appears in the later FedBacys formulation with selective participation (Jeong et al., 14 Nov 2025). Under $M$4-smoothness, unbiased stochastic gradients with bounded variance, bounded gradient divergence, intra-group and inter-group heterogeneity bounds, and optionally a PL condition, the paper derives a bounded stationarity-gap theorem and a PL-based optimization theorem. The participation probability upper bound $M$5 is determined by $M$6, linking convergence directly to charging statistics and training-energy requirements. The transient term in the PL theorem decays as $M$7, but the residual neighborhood depends on $M$8, $M$9, $\bar M$0, $\bar M$1, $\bar M$2, and $\bar M$3.

Other cyclic FL papers are more heuristic or indirect in their theory. CyclicFL does not provide a standard end-to-end FL convergence theorem for the combined P1+P2 procedure; instead it argues that cyclic sequential pre-training better approximates centralized pre-training when task similarity is high and that data-consistent pre-training yields more favorable Lipschitz behavior and flatter basins (Zhang et al., 2023). Cyclic aggregation explicitly states that a mathematical proof is out of scope and that general proofs for cyclic learning rates remain open (Lee et al., 2022). The original FedBacys paper is likewise empirical and intuition-driven rather than theorem-driven (Jeong et al., 16 Apr 2025). CWC is framed around continual-learning regularization and empirical stabilization; the provided material does not give a separate formal convergence theorem for serial FL with consolidation (Song et al., 2024).

5. Empirical behavior across regimes

Cyclic methods are most consistently beneficial in regimes with structured heterogeneity, client drift, or hard resource constraints. In cyclic aggregation, the strongest communication gains are reported on FMNIST and CIFAR-10. For example, the number of rounds required to hit target accuracy on FMNIST drops from $\bar M$4 to $\bar M$5 for FedAvg and from $\bar M$6 to $\bar M$7 for FedProx; on CIFAR-10 it drops from $\bar M$8 to $\bar M$9 for FedAvg and from $\sigma(1),\dots,\sigma(\bar M)$0 to $\sigma(1),\dots,\sigma(\bar M)$1 for both FedProx and MOON (Lee et al., 2022). Final test accuracy also improves, with notable examples including MOON on CIFAR-10, $\sigma(1),\dots,\sigma(\bar M)$2, and FedRS on SVHN, $\sigma(1),\dots,\sigma(\bar M)$3.

CyclicFL reports especially strong effects on difficult non-IID tasks. On CIFAR-100 coarse with $\sigma(1),\dots,\sigma(\bar M)$4, Cyclic+FedAvg reaches $\sigma(1),\dots,\sigma(\bar M)$5 versus FedAvg $\sigma(1),\dots,\sigma(\bar M)$6, a $\sigma(1),\dots,\sigma(\bar M)$7 point gain; on CIFAR-100 fine with $\sigma(1),\dots,\sigma(\bar M)$8, the gain is $\sigma(1),\dots,\sigma(\bar M)$9 versus $(k,i)$0 (Zhang et al., 2023). The same study reports large convergence-speed differences: on CIFAR-10 with $(k,i)$1, Cyclic+FedAvg reaches $(k,i)$2 at round $(k,i)$3, whereas FedAvg reaches $(k,i)$4 at round $(k,i)$5. These findings align with the paper’s interpretation that cyclic pre-training produces a stronger initialization and a flatter loss basin.

CyCP and FedCluster emphasize the role of heterogeneity structure. In the CyCP experiments, higher cycle parameter values improve test accuracy by roughly $(k,i)$6–$(k,i)$7 on FMNIST under stronger heterogeneity and by roughly $(k,i)$8–$(k,i)$9 under milder heterogeneity; training loss also decreases faster for larger cycle parameters (Cho et al., 2023). FedCluster reports faster convergence than conventional FL on CIFAR-10 and MNIST under diverse levels of device-level heterogeneity and for several local optimizers, including SGD with momentum, Adam, and FedProx (Chen et al., 2020).

Serial cyclic FL is most vulnerable to catastrophic forgetting, and CWC is designed precisely for that regime. On MNIST with Dirichlet $\sigma(i)$0, global accuracy improves from $\sigma(i)$1 for CWT to $\sigma(i)$2 for CWC, while FedAvg reaches $\sigma(i)$3; on CIFAR10 with $\sigma(i)$4, CWC improves over CWT from $\sigma(i)$5 to $\sigma(i)$6 (Song et al., 2024). The same paper reports that increasing local epochs is ineffective or unstable for vanilla CWT but helpful for CWC: on MNIST with $\sigma(i)$7, the number of communication rounds to reach $\sigma(i)$8 accuracy is $\sigma(i)$9 for CWT at local epochs $G$0, versus $G$1 for CWC.

EHFL cyclic scheduling is distinguished by explicit energy accounting. The original FedBacys evaluation uses CIFAR-10, $G$2 users, $G$3 epochs, $G$4 slots, $G$5, $G$6, and charging probabilities $G$7 (Jeong et al., 16 Apr 2025). FedBacys reaches faster convergence and higher final test accuracy than baselines for $G$8, while FedAvg attains the highest final average test accuracy at $G$9. In energy consumption, FedBacys has the lowest total energy across charging probabilities and group settings; at $R=\lfloor S/G \rfloor$0, its reported energy is about $R=\lfloor S/G \rfloor$1 battery units versus $R=\lfloor S/G \rfloor$2 for FedAvg, corresponding to roughly $R=\lfloor S/G \rfloor$3–$R=\lfloor S/G \rfloor$4 savings. The later FedBacys-Odd results sharpen the same point: it stabilizes around the same epoch, approximately $R=\lfloor S/G \rfloor$5, as FedBacys while using roughly half the number of local training occurrences when $R=\lfloor S/G \rfloor$6 is large, and at $R=\lfloor S/G \rfloor$7 its total energy is about $R=\lfloor S/G \rfloor$8, far below FedAvg, MIFA, FLDA, and FedBacys (Jeong et al., 14 Nov 2025).

6. Limitations, misconceptions, and open problems

The main conceptual limitation is terminological. “Fed-Cyclic” is not a single established algorithm name but a family resemblance concept spanning periodic aggregation, ordered client traversal, grouped availability, and resource-aware scheduling. Treating all such methods as interchangeable obscures crucial distinctions. Cyclic aggregation changes only the server coefficient; CyclicFL is cyclic only in pre-training; CyCP is a FedAvg participation model; CWT/CWC is serial FL without parallel averaging; FedBacys is EHFL-specific and group-sequential (Lee et al., 2022, Zhang et al., 2023, Cho et al., 2023, Song et al., 2024, Jeong et al., 16 Apr 2025).

A second misconception is that cyclicity always implies deterministic fairness rotation. Several papers contradict that reading. CyCP still performs random sampling within the currently available group (Cho et al., 2023). FedCluster reshuffles cluster order each round in its theory (Chen et al., 2020). FedBacys is periodic at the group level but conditional at the client level, since clients participate only if battery and pending-update conditions are satisfied (Jeong et al., 16 Apr 2025). FedBacys-Odd adds selective participation on odd-numbered eligible opportunities, which further decouples cyclic opportunity from actual participation (Jeong et al., 14 Nov 2025).

Method-specific limitations remain substantial. Cyclic aggregation depends on tuning amplitude $R=\lfloor S/G \rfloor$9 and frequency $$\theta_{i_g+1} \leftarrow \gamma_{\text{cyclic}(i_g)} \cdot ServerOpt(\{\theta_{i_g}^m\}_{m=1}^{M}),$$00, provides no formal convergence theorem, and uses a cyclic-rate expression with a notational inconsistency in the paper (Lee et al., 2022). CyclicFL introduces a front-loaded communication stage and depends on data consistency between cyclic pre-training and downstream FL; its own text also notes that SCAFFOLD can outperform Cyclic+FedAvg on CIFAR-10 (Zhang et al., 2023). CyCP relies on fixed disjoint equal-sized groups and smooth PL objectives, which are restrictive abstractions for deep networks (Cho et al., 2023). FedCluster’s theory assumes full participation within the active cluster and its gains depend on the clustering strategy and the number of clusters $$\theta_{i_g+1} \leftarrow \gamma_{\text{cyclic}(i_g)} \cdot ServerOpt(\{\theta_{i_g}^m\}_{m=1}^{M}),$$01 (Chen et al., 2020). CWC introduces model-sized auxiliary state and hyperparameters $$\theta_{i_g+1} \leftarrow \gamma_{\text{cyclic}(i_g)} \cdot ServerOpt(\{\theta_{i_g}^m\}_{m=1}^{M}),$$02 and $$\theta_{i_g+1} \leftarrow \gamma_{\text{cyclic}(i_g)} \cdot ServerOpt(\{\theta_{i_g}^m\}_{m=1}^{M}),$$03, and its experiments use only four clients (Song et al., 2024). FedBacys shows fluctuations before saturation, exposes a mismatch between its conceptual battery-aware grouping and the pseudocode’s random slicing, and in its original form does not solve an explicit optimization problem over grouping or hub selection (Jeong et al., 16 Apr 2025).

Open directions are correspondingly diverse. The cyclic-aggregation paper identifies hyperparameter optimization as future work (Lee et al., 2022). CyCP points toward more general group structures and non-PL objectives (Cho et al., 2023). FedCluster leaves clustering policy, cluster order, and partial-participation theory only partially resolved (Chen et al., 2020). CWC suggests unresolved scaling and client-order effects in serial FL (Song et al., 2024). FedBacys highlights semantics-aware participation, the interaction among battery capacity, training cost $$\theta_{i_g+1} \leftarrow \gamma_{\text{cyclic}(i_g)} \cdot ServerOpt(\{\theta_{i_g}^m\}_{m=1}^{M}),$$04, and charging probability, and more adaptive EHFL designs (Jeong et al., 16 Apr 2025). The selective-participation extension suggests a broader research program in which cyclic opportunity structures are combined with explicit computation budgeting rather than interpreted as rigid participation mandates (Jeong et al., 14 Nov 2025).