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SoteriaFL Unified Framework for Private Federated Learning with Shifted Communication Compression

Algorithms AIMech:SoteriaFlUnifiedFrameworkForPrivateFederatedLearningWithShiftedCommunicationCompression DRAFT

Aliases: SoteriaFL, Soteria-SGD, Soteria-SVRG, Soteria-SAGA

A unified framework for local differentially private (LDP) federated learning with communication compression (Algorithm 1) in which each client i perturbs its local stochastic gradient estimator tilde{g}_i^t relative to a maintained local reference shift s_i^t via Gaussian noise xi_i^t ~ N(0, sigma_p^2 I_d) before applying an unbiased omega-compressor C_i^t(tilde{g}_i^t - s_i^t + xi_i^t), updating the shift as s_i^{t+1} = s_i^t + gamma_t C_i^t(tilde{g}_i^t - s_i^t + xi_i^t) with optimal shift step size gamma_t = ((1+omega) - sqrt((1+omega)^2 - tau)) / (2*omega*(1+omega)) so that compression variance does not blow up under differential privacy noise.

Identity Notes & Concept Scope Distinct from naive Compressed-DP-SGD (which sets s_i^t = 0 and suffers an O((1+omega) sigma_p^2) noise amplification combined with unbounded gradient-norm variance) and from non-private DIANA / EF21. SoteriaFL (Li, Zhao, Li, & Chi, NeurIPS 2022, arXiv:2206.09888) unifies Soteria-SGD, Soteria-SVRG, and Soteria-SAGA under Lemma 1's shifted-compression contraction.

Claims & Grounded Evidence

4 Claims

Mechanism #soteriafl-shifted-ldp-compressed-gradient-estimator-and-lemma1-contraction-mechanism

In SoteriaFL (Algorithm 1), each client i computes a local gradient estimator tilde{g}_i^t (instantiated as clipped mini-batch SGD, clipped SVRG, or clipped SAGA in Table 2), adds Gaussian LDP noise xi_i^t ~ N(0, sigma_p^2 I_d) to the shifted difference tilde{g}_i^t - s_i^t, transmits v_i^t = C_i^t(tilde{g}_i^t - s_i^t + xi_i^t), and updates s_i^{t+1} = s_i^t + gamma_t v_i^t; by Lemma 1, setting gamma_t = ((1+omega) - sqrt((1+omega)^2 - tau)) / (2*omega*(1+omega)) contracts the shift error Phi_s^t at rate (1 - tau/(4*(1+omega))) while bounding the additive LDP noise term by (1 + 2*(1 - sqrt(1 - tau/(1+omega)^2))) d sigma_p^2.

supports Source: SoteriaFL: A Unified Framework for Private Federated Learning with Communication Compression · Locator: Section 3 Algorithm 1 p. 4 & Section 4 Lemma 1 Equations (5)-(6) p. 6

Scope #soteriafl-eps-delta-ldp-privacy-utility-and-communication-complexity-scope

Under (eps, delta)-local differential privacy (Theorem 1, setting sigma_p^2 = 8 G^2 T log(1/delta) / (K^2 m^2 eps^2)) and L-smoothness (Assumption 1), SoteriaFL (Theorem 2 & Corollaries 1-3) achieves optimal utility O(sqrt(d log(1/delta)) / (n sqrt(m) eps)) with O((1+omega)^{3/2} sqrt(n) m eps) communication rounds for Soteria-SVRG/SAGA when omega <= O(m eps^2 / (d log(1/delta)) - 1), matching uncompressed private FL utility while reducing communicated bits by factor 1/(1+omega).

supports Source: SoteriaFL: A Unified Framework for Private Federated Learning with Communication Compression · Locator: Section 4 Theorems 1-2 & Corollaries 1-3 pp. 5-8, Table 1 p. 2
supports Source: SoteriaFL: A Unified Framework for Private Federated Learning with Communication Compression (arXiv abstract) · Locator: Abstract

Limitation #soteriafl-gradient-clipping-norm-bound-and-unbiased-compressor-limitation

Requires bounded per-sample gradient sensitivity ||nabla f_{i,j}(x)||_2 <= G (enforced via gradient clipping before forming tilde{g}_i^t) to guarantee (eps, delta)-LDP and assumes unbiased omega-compression operators (Assumption 3).

supports Source: SoteriaFL: A Unified Framework for Private Federated Learning with Communication Compression · Locator: Section 2.2 Assumptions 3-4 p. 4 & Section 3.1 Table 2 p. 5

Application #soteriafl-differentially-private-compressed-federated-classification-application

Applied to locally differentially private and communication-compressed federated logistic regression and neural network classification across distributed client datasets.

supports Source: SoteriaFL: A Unified Framework for Private Federated Learning with Communication Compression · Locator: Section 5 Experiments pp. 9-10

⚠️ Curated Limitations & Negative Results

Requires bounded per-sample gradient norm sensitivity ||nabla f_{i,j}(x)||_2 <= G via clipping.
Assumes unbiased omega-compression operators for the theoretical privacy-utility-communication guarantees.

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes

AIO Target Class	Mapping Relation	Mapping Rationale
`AIO:FederatedLearning` Federated Learning	narrow_match	SoteriaFL is a specific locally differentially private and communication-compressed federated learning framework.

Evidence Sources & Primary Literature

3 Sources

Source ID	Publication / Document	Type / Access	Reference & Checksum
`r561-primary-pdf`	SoteriaFL: A Unified Framework for Private Federated Learning with Communication Compression Zhize Li, Haoyu Zhao, Boyue Li, Yuejie Chi	primary paper full_text	ID: https://api.openalex.org/works/https://doi.org/10.52202/068431-0310 sha256:ef533269c03b…
`r561-arxiv-abs`	SoteriaFL: A Unified Framework for Private Federated Learning with Communication Compression (arXiv abstract) Zhize Li, Haoyu Zhao, Boyue Li, Yuejie Chi	primary paper abstract_only	ID: https://arxiv.org/abs/2206.09888 sha256:1e2709946e8c…
`r561-metadata-cr`	SoteriaFL: A Unified Framework for Private Federated Learning with Communication Compression (Crossref metadata) Zhize Li, Haoyu Zhao, Boyue Li, Yuejie Chi	primary paper abstract_only	ID: https://api.openalex.org/works/https://doi.org/10.52202/068431-0310 sha256:8b7ce1ebf18e…

Ontology & Grounding Topology

Open in interactive network graph →

Curation Provenance

Curator: Antigravity

Method: ai_assisted

Model: Gemini

Created: 2026-10-19T10:44:00Z

Updated: 2026-10-19T10:44:00Z

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

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