Age-Weighted FedSGD

• Age-Weighted FedSGD is a design principle that uses age metrics to assess update staleness and guide selective gradient or client participation.
• It integrates methods at multiple levels—coordinate, client, and device—via mechanisms like Top‑k selection, worker scheduling, and residual memory to balance new and stale information.
• Empirical and theoretical analyses show that age-based strategies enhance convergence rates and communication efficiency, especially under resource and selection constraints.

Searching arXiv for the specified paper and closely related work on age-aware federated optimization. First, retrieving the main paper on age-aware partial gradient updates over the air. Now retrieving related papers on age-aware weighting, scheduling, and gradient freshness in federated learning. Age-Weighted FedSGD denotes a family of FedSGD-style federated optimization schemes in which the server uses an age, staleness, or Age-of-Information variable to modulate which updates are requested, how they are aggregated, or when clients are scheduled. In current work, this age variable is not unique: it may count rounds since a model coordinate was last updated, consecutive rounds a worker was idle, the staleness of a client’s data relative to deployment time, the backlog of uncommunicated gradient mass, or the freshness of asynchronously received updates (Du et al., 2 Apr 2025). This suggests that Age-Weighted FedSGD is best understood as a design principle rather than a single standardized optimizer, with concrete realizations spanning coordinate sparsification, client selection, explicit gradient weighting, and communication-system co-design (Wang et al., 2024).

1. Age as a federated optimization signal

The literature instantiates “age” at several levels of granularity. In "Age-Aware Partial Gradient Update Strategy for Federated Learning Over the Air" (Du et al., 2 Apr 2025) and "$r$Age-$k$: Communication-Efficient Federated Learning Using Age Factor" (Mortaheb et al., 2024), age is coordinate-wise and records how many global rounds have elapsed since a parameter index was last updated. In "Communication-Efficient Local SGD with Age-Based Worker Selection" (Zhu et al., 2022), age is worker-wise and equals the number of consecutive rounds that a worker has not been selected. In "Exploring Age-of-Information Weighting in Federated Learning under Data Heterogeneity" (Wang et al., 2024), age is device AoI, updated as $A_n^\mathrm{(t)}=1$ if device $n$ was selected in the previous round and $A_n^\mathrm{(t)}=A_n^\mathrm{(t-1)}+1$ otherwise. In "Age Aware Scheduling for Differentially-Private Federated Learning" (Lin et al., 2024), age is the staleness of the data itself, $a_i=t_{\text{agg}}-t_{c,i}$. In "Age-of-Gradient Updates for Federated Learning over Random Access Channels" (Wu et al., 2024), freshness is measured by the norm $\|\mathbf{g}_n^{(u)}+\mathbf{m}_n^{(u)}\|_2$, where $\mathbf{m}_n^{(u)}$ is an error-feedback memory. In "Inverse Probability Weighting and Age-of-Information Aggregation for Decentralized Federated Learning under Partial Reception" (Kaluannakkage et al., 9 Jun 2026), AoI is continuous-time and defined by $$\mathrm{AoI}_{ij}=\max(0,t_{\mathrm{ref}}-t_{\mathrm{gen}}^j)$$.

Mechanism family	Age variable	Operational role
AgeTop-$k$, $k$0Age-$k$1	Coordinate rounds-since-update	Coordinate selection
AgeSel	Worker idle rounds	Worker selection
AWU	Device AoI	Gradient weighting
AoG	$k$2	Participation threshold
Age-aware DP scheduling	$k$3	Data collection scheduling
DFL-AA	Continuous-time AoI	Aggregation weighting

A common misconception is that age in federated optimization refers only to asynchronous stale client updates. The cited works show that age may instead be a parameter-level staleness process, a client participation history, a data-drift variable, or a residual-information backlog. Another misconception is that age weighting must mean explicit scalar multiplication of a gradient. In several schemes, age enters through hard selection rather than continuous weights: older coordinates or workers are selected more often, while unselected entities receive implicit weight $k$4 in that round (Du et al., 2 Apr 2025).

2. Coordinate-level age weighting and partial-gradient FedSGD

The most direct recent realization of Age-Weighted FedSGD is coordinate-level sparsified aggregation. In the over-the-air setting of (Du et al., 2 Apr 2025), the system comprises an edge server and multiple clients collaborating to minimize

$k$5

with local gradients $k$6. Because the number of available orthogonal carriers is $k$7, only $k$8 coordinates can be transmitted per round. The server therefore maintains an age vector $k$9, updated coordinate-wise as

$A_n^\mathrm{(t)}=1$0

Selection is two-stage: $A_n^\mathrm{(t)}=1$1 The first stage restricts attention to large-magnitude coordinates; the second picks the $A_n^\mathrm{(t)}=1$2 oldest among them. The server then updates only those coordinates, using

$A_n^\mathrm{(t)}=1$3

where $A_n^\mathrm{(t)}=1$4 is the decompressed aggregated OTA signal (Du et al., 2 Apr 2025).

The same basic construction appears in "$A_n^\mathrm{(t)}=1$5Age-$A_n^\mathrm{(t)}=1$6" (Mortaheb et al., 2024). There, each client computes a full gradient $A_n^\mathrm{(t)}=1$7, constructs a sparse vector $A_n^\mathrm{(t)}=1$8, and the server aggregates $A_n^\mathrm{(t)}=1$9. The $n$0Age-$n$1 function first chooses the top-$n$2 largest-magnitude coordinates, then selects the $n$3 coordinates with largest age among those $n$4, increments all ages by $n$5, and resets the selected ages to $n$6. In both papers, age acts as a fairness-inducing control against repeated concentration on the same coordinates. This can be viewed as a binary coordinate-wise age weighting: selected coordinates are updated, unselected coordinates are frozen for that round.

The edge-blind OTA variant in (Elshazly et al., 2 Feb 2026) keeps the same AgeTop-$n$7 logic but places it inside a multi-antenna OFDM uplink. The parameter server maintains a global update buffer $n$8 and an AoI vector $n$9, forms $A_n^\mathrm{(t)}=A_n^\mathrm{(t-1)}+1$0 from the $A_n^\mathrm{(t)}=A_n^\mathrm{(t-1)}+1$1 largest-magnitude coordinates of the buffer, then defines $A_n^\mathrm{(t)}=A_n^\mathrm{(t-1)}+1$2 as the $A_n^\mathrm{(t)}=A_n^\mathrm{(t-1)}+1$3 largest-age indices inside $A_n^\mathrm{(t)}=A_n^\mathrm{(t-1)}+1$4. After decompression of the OTA aggregate, the server updates

$A_n^\mathrm{(t)}=A_n^\mathrm{(t-1)}+1$5

refreshes the selected entries of $A_n^\mathrm{(t)}=A_n^\mathrm{(t-1)}+1$6, and resets their ages to $A_n^\mathrm{(t)}=A_n^\mathrm{(t-1)}+1$7 (Elshazly et al., 2 Feb 2026).

3. Client-, worker-, and data-level age weighting

Age can also operate on participants rather than coordinates. In AgeSel, the parameter server maintains a worker-age vector $A_n^\mathrm{(t)}=A_n^\mathrm{(t-1)}+1$8 with

$A_n^\mathrm{(t)}=A_n^\mathrm{(t-1)}+1$9

Workers with $a_i=t_{\text{agg}}-t_{c,i}$0 are treated as infrequent and prioritized; if there are more such workers than the participation budget $a_i=t_{\text{agg}}-t_{c,i}$1, AgeSel chooses the $a_i=t_{\text{agg}}-t_{c,i}$2 largest ages, tie-breaking by larger dataset size $a_i=t_{\text{agg}}-t_{c,i}$3. Aggregation itself remains uniform: $a_i=t_{\text{agg}}-t_{c,i}$4 Thus age affects who participates, not how selected workers are averaged (Zhu et al., 2022).

A more literal age-weighted FedSGD appears in CAFe’s Age Weighted Update. There the server tracks the instantaneous age $a_i=t_{\text{agg}}-t_{c,i}$5 of client $a_i=t_{\text{agg}}-t_{c,i}$6 at the parameter server and uses a bounded increasing function $a_i=t_{\text{agg}}-t_{c,i}$7. With $a_i=t_{\text{agg}}-t_{c,i}$8, the update is

$a_i=t_{\text{agg}}-t_{c,i}$9

This is an explicit per-client age-weighted FedSGD rule: clients with larger age receive larger weight when they finally contribute (Liyanaarachchi et al., 2024).

The device-AoI formulation of (Wang et al., 2024) is similar in spirit but normalizes the weights to preserve average scale. For selected devices $\|\mathbf{g}_n^{(u)}+\mathbf{m}_n^{(u)}\|_2$0,

$\|\mathbf{g}_n^{(u)}+\mathbf{m}_n^{(u)}\|_2$1

and the age-weighted global loss is

$\|\mathbf{g}_n^{(u)}+\mathbf{m}_n^{(u)}\|_2$2

The server update becomes

$\|\mathbf{g}_n^{(u)}+\mathbf{m}_n^{(u)}\|_2$3

Here age weighting is meant to counteract the accumulated gradient error induced by random device selection under non-IID data (Wang et al., 2024).

The age-aware differentially private scheduling framework of (Lin et al., 2024) uses a different object of age: the staleness of local data relative to a fixed aggregation time, $\|\mathbf{g}_n^{(u)}+\mathbf{m}_n^{(u)}\|_2$4. The server chooses data collection times $\|\mathbf{g}_n^{(u)}+\mathbf{m}_n^{(u)}\|_2$5 and client DP parameters $\|\mathbf{g}_n^{(u)}+\mathbf{m}_n^{(u)}\|_2$6 to minimize the expected loss difference between a practical age-affected, DP-perturbed model and the oracle fresh, non-private model, subject to an age-dependent privacy budget. This is not an update-weighting rule in the narrow sense, but it is an age-aware FedSGD design principle because scheduling determines which data vintages contribute to the aggregated model (Lin et al., 2024).

4. Freshness via residual memory, random access, and asynchronous AoI

A distinct line of work replaces explicit round counters with state-dependent freshness metrics. In AoG for random access FL, each user maintains a memory vector

$\|\mathbf{g}_n^{(u)}+\mathbf{m}_n^{(u)}\|_2$7

where $\|\mathbf{g}_n^{(u)}+\mathbf{m}_n^{(u)}\|_2$8 stores either compression residual or the entire uncommunicated gradient if the user did not participate. The freshness metric is

$\|\mathbf{g}_n^{(u)}+\mathbf{m}_n^{(u)}\|_2$9

and a user becomes active if

$\mathbf{m}_n^{(u)}$0

Active users transmit $\mathbf{m}_n^{(u)}$1, and the server updates

$\mathbf{m}_n^{(u)}$2

Here age is not a counter but the accumulated, un-transmitted gradient mass. This suggests a broader interpretation of age weighting as weighting by pending information rather than by elapsed rounds (Wu et al., 2024).

The decentralized DFL-AA framework uses continuous-time AoI and inverse-probability weighting under partial reception. Each message carries a generation timestamp $\mathbf{m}_n^{(u)}$3; at node $\mathbf{m}_n^{(u)}$4, the reference time is $\mathbf{m}_n^{(u)}$5, and update staleness is

$\mathbf{m}_n^{(u)}$6

AoI enters through an exponential decay factor

$\mathbf{m}_n^{(u)}$7

combined with inverse-probability weighting based on an EWMA estimate of link quality. The paper shows that DFL-AA removes link-quality distortion in expectation and uses AoI-based weighting to mitigate staleness without requiring global synchronization (Kaluannakkage et al., 9 Jun 2026). Although the setting is decentralized model averaging rather than centralized FedSGD, the mechanism ports directly to asynchronous FedSGD: age can be treated as a continuous-time decay on client contributions.

These formulations clarify that age-aware aggregation need not be tied to a strict notion of “last selected round.” It may instead encode how much gradient information is backlogged, how old a received message is in wall-clock time, or how much distortion an update has experienced in transit. This widens the scope of Age-Weighted FedSGD beyond synchronous sampling policies.

5. Convergence analyses and compression/error models

Theoretical treatments of age-aware federated optimization share a common structure: age affects a bias, compression, or sampling term, while the underlying FedSGD-like dynamics retain standard $\mathbf{m}_n^{(u)}$8, $\mathbf{m}_n^{(u)}$9, or $$\mathrm{AoI}_{ij}=\max(0,t_{\mathrm{ref}}-t_{\mathrm{gen}}^j)$$0 forms.

For AgeTop-$$\mathrm{AoI}_{ij}=\max(0,t_{\mathrm{ref}}-t_{\mathrm{gen}}^j)$$1 over the air, (Du et al., 2 Apr 2025) proves

$$\mathrm{AoI}_{ij}=\max(0,t_{\mathrm{ref}}-t_{\mathrm{gen}}^j)$$2

with

$$\mathrm{AoI}_{ij}=\max(0,t_{\mathrm{ref}}-t_{\mathrm{gen}}^j)$$3

The compression factor is

$$\mathrm{AoI}_{ij}=\max(0,t_{\mathrm{ref}}-t_{\mathrm{gen}}^j)$$4

The rate is $$\mathrm{AoI}_{ij}=\max(0,t_{\mathrm{ref}}-t_{\mathrm{gen}}^j)$$5 in average squared gradient norm, while $$\mathrm{AoI}_{ij}=\max(0,t_{\mathrm{ref}}-t_{\mathrm{gen}}^j)$$6 quantifies how partial coordinate selection affects the residual error (Du et al., 2 Apr 2025).

The same $$\mathrm{AoI}_{ij}=\max(0,t_{\mathrm{ref}}-t_{\mathrm{gen}}^j)$$7 expression appears in $$\mathrm{AoI}_{ij}=\max(0,t_{\mathrm{ref}}-t_{\mathrm{gen}}^j)$$8Age-$$\mathrm{AoI}_{ij}=\max(0,t_{\mathrm{ref}}-t_{\mathrm{gen}}^j)$$9, where the age-based sparsifier is analyzed as a compression operator satisfying

$k$0

Because $k$1Age-$k$2 is a valid compressor, it inherits the $k$3 convergence guarantees of compressed SGD (Mortaheb et al., 2024). In the edge-blind OTA formulation, the convergence bound contains both a compression term proportional to $k$4 and a channel-noise term proportional to $k$5, making explicit the trade-off between updating more coordinates and accumulating more noise (Elshazly et al., 2 Feb 2026).

At the worker-selection level, AgeSel establishes

$k$6

so the method retains the standard $k$7 sublinear rate for non-convex local SGD with partial participation. The distinguishing constant is the traversal parameter $k$8: smaller $k$9 implies smaller $k$00, which improves the constant $k$01 by forcing workers to participate more regularly (Zhu et al., 2022).

CAFe makes age appear explicitly in the convergence rate. Its MCU scheme yields

$k$02

and since the average client age is

$k$03

the rate is equivalently

$k$04

Age is therefore not merely a heuristic monitoring variable; it enters as a multiplicative factor in the asymptotic bound (Liyanaarachchi et al., 2024).

The AoI-weighted formulation of (Wang et al., 2024) derives a PL-based convergence bound

$k$05

where $k$06 is the age-weighted gradient error relative to full participation. The formal role of age is to reduce the mismatch between selected-device and full-population distributions, thereby shrinking $k$07 (Wang et al., 2024).

6. Communication systems, empirical behavior, and practical design trade-offs

Across implementations, age-aware methods are most beneficial when communication constraints induce repeated omission of some information. In OTA partial-gradient FL, experiments on MNIST and CIFAR-10 show that AgeTop-$k$08 achieves higher final test accuracy and more stable convergence curves than rTop-$k$09; with $k$10 fixed on MNIST, increasing $k$11 from $k$12 to $k$13 to $k$14 improves convergence speed, while with $k$15 fixed, increasing $k$16 from $k$17 to $k$18 to $k$19 slows convergence (Du et al., 2 Apr 2025). In the edge-blind multi-antenna OTA system, experimental results show that more parameter-server antennas greatly improve accuracy and convergence speed, that AgeTop-$k$20 outperforms random selection under relatively good channel conditions, and that the optimum $k$21 depends on the channel, with smaller $k$22 being better in noisy settings (Elshazly et al., 2 Feb 2026).

In random-access FL, AoG almost matches genie-aided performance for $k$23 while remaining fully distributed and low-overhead, and $k$24 memory accumulation is significantly better than $k$25 because memory is what makes the freshness metric meaningfully encode backlog (Wu et al., 2024). In local SGD with worker ages, AgeSel on non-IID EMNIST with $k$26, $k$27, and $k$28 reduces the number of training rounds and total communication cost relative to FedAvg and Round Robin, while also being more communication-efficient than OCS because OCS requires all $k$29 workers to download the global model each round (Zhu et al., 2022).

The system-level age perspective of CAFe shows that age interacts with latency control. For fixed $k$30, $k$31 minimizes average age, communication cost, and resource wastage in the homogeneous low-variance regime, and the scalarized objective

$k$32

is used to select $k$33 (Liyanaarachchi et al., 2024). Under biased fast clients, its Age Weighted Update substantially outperforms MCU, because it downweights frequently contributing clients and upweights stale ones (Liyanaarachchi et al., 2024). In the wireless non-IID system of (Wang et al., 2024), Age-Weighted FedSGD consistently converges faster and to higher accuracy than conventional FedSGD; on CIFAR-10, the matching-based sub-channel assignment increases the average number of selected devices per round from $k$34 to $k$35, about $k$36 more devices per round, which further improves convergence (Wang et al., 2024).

These results support several stable design conclusions. First, age weighting is most useful when device or coordinate starvation is systematic rather than incidental. Second, age should usually be coupled with another importance signal: gradient magnitude in AgeTop-$k$37, dataset size in AgeSel, or resource feasibility in wireless scheduling. Third, aggressive use of age alone can be counterproductive if it ignores noise, heterogeneity, or channel conditions. This explains why the strongest methods are hybrid constructions: magnitude-plus-age, participation-plus-age, or AoI-plus-IPW.

7. Conceptual boundaries, misconceptions, and open directions

Age-Weighted FedSGD is sometimes conflated with asynchronous stale-gradient correction. The literature is broader. Some methods weight clients directly by age (Liyanaarachchi et al., 2024); some select long-idle workers but still average selected updates uniformly (Zhu et al., 2022); some never introduce explicit age scalars and instead use age to choose coordinates (Du et al., 2 Apr 2025); and some replace counters entirely with residual memory norms or timestamp-derived AoI (Wu et al., 2024). A plausible implication is that “weighting” should be read functionally: any mechanism that increases the expected influence of stale-but-relevant information qualifies, even if the implementation is a threshold or a sparsifier rather than a continuous coefficient.

Another recurring issue is what age is trying to correct. In non-IID sampling, it targets accumulated gradient bias and weight divergence (Wang et al., 2024). In partial communication, it targets starvation of coordinates or clients (Du et al., 2 Apr 2025). In differentially private scheduling, it enters a three-way tradeoff among age, accuracy, and differential privacy (Lin et al., 2024). In lossy decentralized learning, it is paired with inverse-probability weighting because staleness and link-quality bias are distinct effects (Kaluannakkage et al., 9 Jun 2026). This suggests that age alone is rarely sufficient; it is usually one factor in a multi-criterion aggregation rule.

The main open directions stated or implied across the cited works are extensions to asynchronous FL, more realistic wireless channels, stronger privacy accountants in multi-round settings, soft age-weight functions instead of hard top-$k$38 selection, and joint treatment of age with heterogeneity, variance reduction, or robust aggregation (Lin et al., 2024). Current evidence consistently supports age as a first-class signal under communication constraints, but the optimal form of age weighting remains architecture- and system-dependent.