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q-Fair Federated Learning (q-FFL) and q-FedAvg for Alpha-Fair Resource Allocation

Algorithms AIMech:QFairFederatedLearningAlphaFairResourceAllocation DRAFT

Aliases: q-FFL, q-Fair Federated Learning, q-FedAvg, q-FedSGD, q-MAML

A fairness-aware federated optimization formulation (q-Fair Federated Learning, q-FFL) and its communication-efficient solver (q-FedAvg) inspired by alpha-fair resource allocation in wireless networks, which minimizes the reweighted aggregate objective f_q(w) = sum_{k=1}^m (p_k / (q + 1)) F_k^{q+1}(w) across m devices with non-negative local losses F_k(w) and tunable fairness exponent q >= 0, continuously interpolating between standard Federated Averaging (q = 0) and minimax Agnostic Federated Learning (q -> infinity). Using an analytical local Lipschitz upper bound L_q(w) = L F_k(w)^q + q F_k(w)^{q-1} ||nabla F_k(w)||^2 derived from the base smoothness constant L at q = 0, q-FedSGD and q-FedAvg dynamically scale device updates Delta_k = F_k^q(w^t) Delta_k^t by the denominator sum_k h_k^t without retuning learning rates for each q.

Identity Notes & Concept Scope Distinct from standard Federated Averaging (AIMech:FederatedAveragingClientServerOptimization, which is the q = 0 special case that minimizes average loss without controlling cross-device accuracy variance) and from Ditto (AIMech:DittoFairAndRobustPersonalizedFederatedMultiTaskLearning, which achieves device fairness via personalized models v_k regularized toward w^* rather than learning a single fair global model w via (q+1)-power loss reweighting).

Claims & Grounded Evidence

4 Claims

Mechanism #r394-local-lipschitz-hessian-bound-and-dynamic-step-size

Lemma 3 proves that for any non-negative L-smooth function f(w), the gradient of f_q(w) = f(w)^{q+1}/(q+1) is nabla f_q(w) = f(w)^q nabla f(w) with Hessian nabla^2 f_q(w) = q f(w)^{q-1} nabla f(w) nabla f(w)^T + f(w)^q nabla^2 f(w), whose spectral norm at w is upper-bounded by L_q(w) = L f(w)^q + q f(w)^{q-1} ||nabla f(w)||^2; substituting the heuristic local update Delta_k^t = L(w^t - w_bar_k^{t+1}) for nabla F_k(w^t) in q-FedAvg (Algorithm 2) yields h_k^t = q F_k^{q-1}(w^t)||Delta_k^t||^2 + L F_k^q(w^t), allowing a single tuned step size 1/L at q = 0 to transfer across all q > 0.

supports Source: Fair Resource Allocation in Federated Learning · Locator: Section 3.3 Improving Communication Efficiency: q-FedAvg (Lemma 3, Algorithms 1-2), pp. 4-6

Mechanism #r394-uniformity-interpolation-and-variance-reduction

Under Definition 1 (fairness via uniformity of test accuracy distribution across devices) and Appendix B.2 Lemmas 4-6, increasing q >= 0 amplifies relative gradient contributions from higher-loss devices as (F_i(w) / F_j(w))^q, monotonically decreasing the generalization error of the worst-performing device and tightening the cross-device accuracy variance.

supports Source: Fair Resource Allocation in Federated Learning · Locator: Section 3.1 Definition 1, Section 3.2 Eq. (2), and Appendix B.2 Properties of the q-FFL Objective (Lemmas 4-6), pp. 3-4, 15-16

Limitation #r394-nonnegative-loss-and-mean-worst-tradeoff-limitation

Requires local objective functions F_k(w) >= 0 so F_k^{q+1}(w) preserves convexity/monotonicity, and replacing nabla F_k(w^t) by L(w^t - w_bar_k^{t+1}) in q-FedAvg is a heuristic approximation when multiple local SGD steps are taken; moreover, overly large q prioritizes noisy or outlier devices at the expense of mean global accuracy.

supports Source: Fair Resource Allocation in Federated Learning · Locator: Section 3.2-3.3 and Section 4.2 Choosing q, pp. 4-8

Application #r394-federated-benchmarks-and-q-maml-application

Applied to Federated Extended MNIST (FEMNIST), Vehicle sensor classification, Sent140 Twitter sentiment analysis, Shakespeare RNN, and Omniglot meta-learning via q-MAML (Algorithm 4), reducing cross-device test accuracy variance by an average of 45% while maintaining mean accuracy.

supports Source: Fair Resource Allocation in Federated Learning · Locator: Section 4 Evaluation (Table 1, Figures 1-4) and Appendix D Algorithm 4 (q-MAML), pp. 6-9, 18-19

⚠️ Curated Limitations & Negative Results

Requires non-negative local loss functions F_k(w) >= 0.
Susceptible to corrupt or noisy outlier devices whose artificially high losses F_k(w)^q receive amplified weights as q increases.

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes

AIO Target Class	Mapping Relation	Mapping Rationale
`AIO:FederatedLearning` Federated Learning	narrow_match	q-Fair Federated Learning (q-FFL) and q-FedAvg are fairness-reweighted federated optimization methods within FederatedLearning.

Evidence Sources & Primary Literature

3 Sources

Source ID	Publication / Document	Type / Access	Reference & Checksum
`r394-primary-pdf`	Fair Resource Allocation in Federated Learning Tian Li, Maziar Sanjabi, Ahmad Beirami, Virginia Smith	primary paper full_text	ID: https://doi.org/10.48550/arXiv.1905.10497 sha256:6adecbef0cb8…
`r394-arxiv-abs`	Fair Resource Allocation in Federated Learning (arXiv abstract) Tian Li, Maziar Sanjabi, Ahmad Beirami, Virginia Smith	primary paper abstract_only	ID: https://arxiv.org/abs/1905.10497 sha256:d13914235751…
`r394-metadata-cr`	Fair Resource Allocation in Federated Learning (Crossref metadata) Tian Li, Maziar Sanjabi, Ahmad Beirami, Virginia Smith	primary paper abstract_only	ID: https://doi.org/10.48550/arXiv.1905.10497 sha256:940466014f33…

Ontology & Grounding Topology

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Curation Provenance

Curator: Antigravity

Method: ai_assisted

Model: Gemini

Created: 2026-10-19T07:57:00Z

Updated: 2026-10-19T07:57:00Z

Source File: data/curated/QFairFederatedLearningAlphaFairResourceAllocation.yaml · Schema: curated_concept.yaml

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