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Per-FedAvg Model-Agnostic Meta-Learning for Personalized Federated Learning

Algorithms AIMech:PerFedAvgModelAgnosticMetaLearningForPersonalizedFederatedLearning DRAFT

Aliases: Per-FedAvg, Personalized FedAvg, Per-FedAvg (FO), Per-FedAvg (HF)

A personalized federated learning algorithm (Per-FedAvg) grounded in Model-Agnostic Meta-Learning (MAML) that seeks a shared global initialization w in R^d minimizing the average post-adaptation loss F(w) = (1/n) sum_{i=1}^n F_i(w) with F_i(w) = f_i(w - alpha * nabla f_i(w)) for local adaptation step size alpha >= 0. During each communication round, selected clients execute tau local meta-SGD steps using three independent mini-batches (D_i, D'_i, D''_i) to form the stochastic meta-gradient nabla_tilde F_i(w) = (I - alpha * nabla_tilde^2 f_i(w, D''_i)) nabla_tilde f_i(w - alpha * nabla_tilde f_i(w, D_i), D'_i), supported by practical First-Order (Per-FedAvg FO) and finite-difference Hessian-Free (Per-FedAvg HF) approximations.

Identity Notes & Concept Scope Distinct from classical centralized MAML (AIMech:ModelAgnosticMetaLearning, which performs single-step centralized meta-updates across tasks rather than tau multi-step local client updates with bounded client drift and compositional inner-batch bias analysis in federated networks) and from pFedMe (AIMech:PFedMePersonalizedFederatedLearningWithMoreauEnvelopes, which optimizes proximal Moreau envelopes min_{theta_i} {f_i(theta_i) + (lambda/2)||theta_i - w||^2} instead of one-step gradient adaptation f_i(w - alpha nabla f_i(w))).

Claims & Grounded Evidence

4 Claims

Mechanism #r396-meta-objective-smoothness-and-compositional-stochastic-bias

Under L-smooth, B-bounded-gradient, rho-Hessian-Lipschitz nonconvex client losses f_i, Lemma 4.2 proves that each meta-function F_i(w) = f_i(w - alpha nabla f_i(w)) is L_F-smooth with L_F = 4L + alpha * rho * B for alpha in [0, 1/L], while Lemma 4.3 proves that evaluating nabla_tilde f_i at the stochastic inner point w - alpha nabla_tilde f_i(w, D) induces a non-vanishing compositional bias ||E[nabla_tilde F_i(w)] - nabla F_i(w)|| <= alpha * L * sigma_G / sqrt(D) coupled with bounded variance sigma_F^2.

supports Source: Personalized Federated Learning with Theoretical Guarantees: A Model-Agnostic Meta-Learning Approach · Locator: Section 4.1 Assumptions 1-3 and Section 4.2 Lemmas 4.1, 4.2, 4.3, and 4.4, pp. 5-7

Mechanism #r396-nonconvex-stationarity-and-hessian-free-approximation

Theorem 4.5 and Corollary 4.6 prove that Per-FedAvg attains an O(eps + alpha^2 sigma_G^2 / D)-first-order stationary point of F(w) in K = O(eps^{-3/2}) communication rounds with tau = O(eps^{-1/2}) local steps per round; furthermore, Section 5 replaces the exact Hessian-vector product with the two-point finite difference d_i^k = (nabla f_i(w + delta g_adapt) - nabla f_i(w - delta g_adapt)) / (2 delta) with error O(rho delta^2).

supports Source: Personalized Federated Learning with Theoretical Guarantees: A Model-Agnostic Meta-Learning Approach · Locator: Section 4.2 Theorem 4.5 & Corollary 4.6 and Section 5 Practical Implementation, pp. 7-8

Limitation #r396-second-order-derivatives-and-inner-batch-bias-limitation

Exact Per-FedAvg requires computing Hessian-vector products across three separate mini-batches per local step, and its stochastic meta-gradient estimator retains an O(alpha^2 sigma_G^2 / D) stationarity floor unless the inner adaptation batch size D scales as O(alpha^2 / eps) or alpha scales as O(sqrt(eps)).

supports Source: Personalized Federated Learning with Theoretical Guarantees: A Model-Agnostic Meta-Learning Approach · Locator: Section 4.2 Lemma 4.3, Theorem 4.5, and Corollary 4.6, pp. 6-8

Application #r396-heterogeneous-mnist-and-cifar10-personalization-application

Applied to personalized neural network classification on heterogeneous MNIST and CIFAR-10 client partitions, showing that Per-FedAvg (HF) and Per-FedAvg (FO) achieve higher post-adaptation test accuracy than standard FedAvg + one-step fine-tuning.

supports Source: Personalized Federated Learning with Theoretical Guarantees: A Model-Agnostic Meta-Learning Approach · Locator: Section 5 Numerical Experiments (Table 1, Figure 1), pp. 8-9

⚠️ Curated Limitations & Negative Results

Requires three mini-batches per local meta-step and either Hessian-vector products or finite-difference approximations.
Stochastic inner gradient evaluation creates an O(alpha^2 sigma_G^2 / D) compositional bias unless inner batch size D is large.

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes

AIO Target Class	Mapping Relation	Mapping Rationale
`AIO:FederatedLearning` Federated Learning	narrow_match	Per-FedAvg is a MAML-based personalized federated learning algorithm within FederatedLearning.

Evidence Sources & Primary Literature

3 Sources

Source ID	Publication / Document	Type / Access	Reference & Checksum
`r396-primary-pdf`	Personalized Federated Learning with Theoretical Guarantees: A Model-Agnostic Meta-Learning Approach Alireza Fallah, Aryan Mokhtari, Asuman Ozdaglar	primary paper full_text	ID: https://doi.org/10.48550/arXiv.2002.07948 sha256:d2310ea80444…
`r396-arxiv-abs`	Personalized Federated Learning with Theoretical Guarantees: A Model-Agnostic Meta-Learning Approach (arXiv abstract) Alireza Fallah, Aryan Mokhtari, Asuman Ozdaglar	primary paper abstract_only	ID: https://arxiv.org/abs/2002.07948 sha256:a5117167c5f2…
`r396-metadata-cr`	Personalized Federated Learning with Theoretical Guarantees: A Model-Agnostic Meta-Learning Approach (Crossref metadata) Alireza Fallah, Aryan Mokhtari, Asuman Ozdaglar	primary paper abstract_only	ID: https://doi.org/10.48550/arXiv.2002.07948 sha256:68a2bd1c9eea…

Ontology & Grounding Topology

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Curation Provenance

Curator: Antigravity

Method: ai_assisted

Model: Gemini

Created: 2026-10-19T07:59:00Z

Updated: 2026-10-19T07:59:00Z

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

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