A Decentralized Federated Learning Framework via Committee Mechanism with Convergence Guarantee

1 INTRODUCTION

• Federated learning lets clients train a shared model without uploading local source data, while a central server aggregates their gradients.The paper describes each round as local training, gradient upload and aggregation, model update, and redistribution.Source: §1 · p. 1
• Existing serverless FL approaches use P2P, Gossip, or blockchain, but few provide theoretical convergence analysis.The paper identifies this lack of performance guarantees as a gap in prior serverless frameworks.Source: §1 · p. 2
• CMFL uses a serverless committee to monitor aggregation and defend against malicious clients and servers.Committee members screen gradients, and the paper analyzes convergence under its election and selection strategies.Source: §1 · p. 2
• CMFL offers two opposite gradient-selection strategies: one targets robustness, while the other targets faster training in non-attack scenarios.The paper also presents an election strategy and convergence analysis accounting for these strategies.Source: §1 · p. 2
• Experiments report faster convergence and better performance than typical and Byzantine-tolerant FL models.The introduction reports the comparison without specifying particular datasets or numeric results in these passages.Source: §1 · p. 2

2 RELATED WORK

• Prior Non-IID FL work includes convergence guarantees, FedProx, shared-data strategies, client clustering, and methods for heterogeneous data.The cited examples include convergence analysis for FedAvg and accelerated convergence properties for MFL.Source: §2 · p. 2
• Byzantine-tolerant methods use distance-based selection, coordinate-wise median or trimmed mean, or learned gradient-quality scoring, but the cited approaches do not defend against malicious servers.The section describes Krum, Median and Trimmed Mean, and a Hidden Markov Model approach.Source: §2 · p. 3
• Serverless FL approaches imitate P2P or Gossip protocols, or use blockchain, but the paper says they lack convergence analysis and consideration of Byzantine client attacks.Examples include P2P, Gossip, and blockchain approaches.Source: §2 · p. 3
• CMFL is presented as a serverless framework that handles Byzantine attacks on clients and servers, improves Non-IID performance without attacks, and provides convergence analysis.The related-work section contrasts this combination with prior serverless approaches lacking convergence analysis and client-attack consideration.Source: §2 · p. 3

3.1 Federated Learning

• A typical FL round selects clients, distributes the global model, collects local SGD gradients, and aggregates them with FedAvg to update the model.Training repeats until convergence or the model accuracy meets requirements.Source: §3.1 · p. 3

3.2 Problem Formulation

• The formulation assigns each of K clients a local dataset D_k and defines its local objective from a user-defined sample loss.The global objective is introduced, and the local gradient is computed over mini-batches sampled from each client dataset after local SGD.Source: §3.2 · p. 3
• The global gradient aggregates the selected clients’ local gradients using dataset-size weights, and the global model is updated with the global learning rate.For client k in selected set S_t, p_k,S_t = n_k / Σ_{k∈S_t} n_k; η_t denotes the global learning rate.Source: §3.2 · pp. 3–4

4 COMMITTEE MECHANISM BASED FEDERATED LEARNING

• CMFL delegates gradient filtering and aggregation decisions to committee members, whose majority consensus replaces reliance on a central server.The paper states that attacks by malicious clients become meaningless when honest committee members outnumber malicious ones.Source: §4 · p. 4

4.1 Framework of CMFL

• The framework scores training clients, selects qualified gradients for aggregation, elects replacement committee members, and returns former members to the idle pool.Committee clients use a pBFT-inspired consensus protocol for selection, aggregation, and election.Source: §4.1 · p. 4

4.2.1 Scoring System

• The scoring system compares Euclidean distances between training-client and committee gradients, assigning higher scores to honest gradients under the stated assumption.The paper says malicious gradients are expected to score lower when their proportion is within a tolerable range; without attacks, score reflects client heterogeneity.Source: §4.2.1 · p. 5

4.2.2 Selection Strategy

• Selection Strategy I aggregates the top α% of scored gradients to favor robustness, but may exclude clients whose differences represent broader data characteristics.The paper says it is suited to Byzantine-attack scenarios.Source: §4.2.2 · pp. 5–6
• Selection Strategy II aggregates the bottom α% to favor convergence and performance without attacks, but offers no robustness guarantee.The paper warns that malicious gradients may be preferentially used, sharply reducing model performance.Source: §4.2.2 · p. 6

4.2.3 Election Strategy

• The election strategy selects clients near the middle of the score ranking to limit malicious committee membership and avoid overreliance on the initial committee.The stated aims are robustness and system stability; a small malicious minority may still enter the committee.Source: §4.2.3 · p. 6

4.2.4 Committee Consensus Protocol

• The committee consensus protocol has a randomly chosen primary client propose an operation, with replicates checking its client set and results before majority agreement.At least ⌊C/2⌋+1 identical responses are required for consensus; the committee repeats the process for the new committee set and distributes the updated model.Source: §4.2.4 · pp. 6–7

4.3 Training Algorithm

• Each training round samples clients, performs local SGD, scores and verifies gradients, updates the global model after consensus, and elects new committee members.The five-step cycle repeats until convergence or the maximum communication round T.Source: §4.3 · p. 7

5.1.1 Assumptions

• Assumptions 1–2 are standard in FL; Assumption 3 concerns bounded variance between local and global objectives; Assumption 4 is standard in nonconvex optimization; Assumption 5 constrains optimal-objective deviation between aggregation and committee client sets.Source: §5.1.1 · p. 8

5.1.2 Definition

• Client heterogeneity Γ is nonzero in non-IID settings and gradually approaches zero as the number of clients K grows in IID settings.The paper adopts this definition from Li et al..Source: §5.1.2 · p. 8
• The aggregation-committee gap varies with the aggregation client set and model during training, and its upper and lower bounds support a conservative convergence-error bound.The bounds are denoted ϕmax and ϕmin.Source: §5.1.2 · p. 8

5.1.3 Convergence Result and Analysis

• Under Assumptions 1–5 and Definitions 1–2, CMFL’s expected global objective error after T rounds satisfies a bound whose constants include terms affected by selection strategy.The convergence proof is presented in the Supplement.Source: §5.1.3 · pp. 8–9
• Selection strategy I yields low ϕmin and slower convergence, whereas strategy II yields high ϕmin and faster convergence at O(1/(T ϕmin)); strategy I is more appropriate under Byzantine attacks.The framework favors universal clients under strategy I and extreme clients under strategy II.Source: §5.1.3 · p. 9

5.2.1 Computaion Complexity

• CMFL’s computation analysis covers local training, scoring, aggregation, selection, and election, with selection and election overhead described as negligible.The analysis specifies the phases’ computation overheads and assumes parallel local training, scoring, and aggregation.Source: §5.2.1 · p. 9

5.2.2 Communication Complexity

• Communication analysis counts gradient uploads to committee clients and global-model downloads to training clients; committee consensus broadcasting is comparatively negligible.The analysis assumes a maximum transmission rate r and equal maximum bandwidth for each client.Source: §5.2.2 · p. 9
• System heterogeneity remains an open issue: client performance differences affect training time, some clients drop out, and further work is needed.Maximum waiting times or minimum received-gradient thresholds are cited as ways to alleviate performance degradation.Source: §5.2.2 · pp. 9–10

6 EXPERIMENTS

• The evaluation spans normal training, Byzantine robustness, hyperparameter variation, efficiency, and the influence of malicious committee members.For normal training, the setup uses α = 40, ω = 40, and ϵ = 0; the attack comparison uses ϵ = 10.Source: §6 · p. 10, §6.2.1 · p. 10, §6.3.1 · p. 12

6.1.1 Datasets and Models

• The experiments use three real-world distributed datasets under Non-IID settings: FEMNIST, Sentiment140, and Shakespeare.They pair FEMNIST with AlexNet and the two text datasets with LSTM classifiers.Source: §6.1.1 · p. 10

6.2.2 Result Analysis

• In non-attack training, strategy II outperforms typical FL and strategy I, while strategy I has the slowest convergence and lowest accuracy.Strategy II gives low-accuracy clients more aggregation opportunities; under Byzantine attacks, however, strategy I is preferred because low scores can indicate malicious clients.Source: §6.2.2 · pp. 11–12, Figure 2 · p. 11, Figure 3 · p. 13

6.3.1 Experiment Setting

• The Byzantine-resilience comparison tests gradient scaling, same-value, and back-gradient attacks against Median, Trimmed Mean, Krum, and Multi-Krum.The scaling attack multiplies gradient elements by random λ ∈[0.5, 1); the same-value attack uses zeros, and the back-gradient attack reverses gradient direction.Source: §6.3.1 · p. 12

6.3.2 Result Analysis

• Under the tested attacks, CMFL with selection strategy I converges fastest and reaches the highest overall accuracy among the five algorithms, though its accuracy fluctuates more than Median and Multi-Krum.The comparison covers FEMNIST, Sentiment140, and Shakespeare; CMFL is also the only evaluated framework without a central server.Source: §6.3.2 · p. 12, Figure 4 · p. 13, Figure 5 · p. 14

6.4.2 Result Analysis

• Within suitable ranges, increasing committee size or aggregation-client proportion can improve performance, but excessive α, ω, or ϵ can cause a cliff-like decline.The reported example for committee size is α = 10, ϵ ≤30, and ω ≤30; aggregation-client proportion α must remain at or below threshold χ to limit malicious gradients.Source: §6.4.2 · pp. 13, 15, Figure 7 · p. 14

6.5.2 Result Analysis

• CMFL consistently performs better than the other two decentralized FL frameworks, while typical FL performs better overall; its advantage shrinks as transmission rate rises and reverses at 100Mps on Sentiment140.CMFL uses committee clients rather than broadcasting gradients to all clients, reducing communication overhead relative to the other two decentralized frameworks.Source: §6.5.2 · p. 15

6.6.2 Result Analysis

• A small number of malicious committee members can leave scoring effective and improve performance, but too many can destroy scoring and sharply reduce it.With more malicious clients, more may enter the committee; if scoring remains effective, malicious clients still score below honest clients.Source: §6.6.2 · p. 15

7 CONCLUSION

• CMFL combines a serverless committee framework with election and selection strategies, and the paper reports convergence guarantees under Byzantine attacks.The authors state that the strategies address Byzantine attacks and malicious-server problems.Source: §7 · p. 16
• Experiments demonstrate CMFL's outperformance over typical federated learning and Byzantine-tolerant models, supporting its reported effectiveness and robustness.The conclusion does not specify the metrics or settings for this comparison.Source: §7 · p. 16
• Designing election and selection strategies with theoretical guarantees for targeted attacks, including backdoor attacks, remains open.The framework's current robustness mainly relies on detecting abnormal local gradients.Source: §7 · p. 16

A.1 Definition and Lemma

• The analysis indexes total local SGD iterations by t, with local iteration i represented as tτ + i.The notation is introduced for the convergence analysis.Source: §A.1 · p. 19
• Clients use local gradients for local SGD, while the analysis treats the global model as updated each iteration despite actual updates occurring every τ rounds.At iterations divisible by τ, clients download the global model as their new local model.Source: §A.1 · p. 19
• The appendix introduces lemmas on the global-local gradient product and a client heterogeneous bound.The heterogeneous bound is stated under Assumption 4.Source: §A.1 · p. 19

A.2 Proof of Lemma

• The section's stated task is to prove Lemmas 1 through 3.Source: §A.2 · p. 19

A.2.1 Proof of Lemma 1

• The proof introduces the client's local model into the formula.Source: §A.2.1 · p. 20
• The derivation applies the Cauchy-Schwarz and AM-GM inequalities.Source: §A.2.1 · p. 20
• The proof completes the argument by expanding the formula under Assumption 2.Source: §A.2.1 · p. 20

• The proof begins by rewriting the original formula and expanding it in subsequent steps.Source: §A.2.2 · p. 20
• Assumptions 2 and 1 are invoked during the expansion.Source: §A.2.2 · pp. 20–21
• Under the stated condition 2ηt ≤ 1 vt, the proof continues the expansion and concludes.Source: §A.2.2 · p. 21

A.2.3 Proof of Lemma 3

• For indices in S(t), the squared distance term is zero when k = k′, and at most m(m −1) distinct-index pairs remain.Source: §A.2.3 · pp. 21–22
• Selected local models share an update at least every τ epochs, bounding their separation over that interval.The proof also uses non-increasing ηt and ηt0 ≤ 2ηt.Source: §A.2.3 · p. 21

A.3 Proof of Theorem 1

• Theorem 1's proof defines H(w, t + 1) as squared distance from w∗ after the update w(t) − ηtg(t).Source: §A.3 · p. 22
• The proof defines Q(w, k, t), then uses Lemma 3 to express its expectation; subsequent steps invoke Assumption 3, Assumption 5 with Definitions 1–2, and Lemmas 1 and 2.Source: §A.3 · pp. 22–25
• After expanding the terms and solving the expectation, the proof invokes L-smoothness and completes Theorem 1.Source: §A.3 · pp. 24–26