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REVIEW 6 major objections 5 minor 57 references

Centroid Approximation for Byzantine-Tolerant Federated Learning

T0 review · 6 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper proves a first lower bound for box-valid Byzantine-tolerant averaging: every such rule has centroid approximation ratio at least about $\sqrt{\min\{(n-t)/t, d\}}$, with matching upper bounds of $2\sqrt{\min\{n,d\}}$.

desk verdict The paper's advertised box-validity lower bound is contradicted by its own upper bound; the underlying ideas are new and possibly fixable, but the write-up needs major repair. read the letter →

arxiv 2506.15264 v1 pith:S56T3FRX submitted 2025-06-18 cs.LG cs.DC

Mélanie Cambus , Darya Melnyk , Tijana Milentijević , Stefan Schmid This is my paper · ORCID
classification cs.LGcs.DC
keywords Byzantinefaulttolerancefederatedlearningcentroidapproximationboxvalidityconvextrimmedtrustedhyperboxrobustaggregationapproximateagreement
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper studies a federated-learning server that averages client updates when up to $t$ of $n$ clients may be Byzantine. It measures an aggregation rule by its centroid approximation ratio: the distance from the rule's output to the true average of the honest clients, divided by the radius of the smallest ball that contains the average of every possible subset of $n-t$ clients. The central claim is that the widely used box validity condition---the rule must output inside the coordinate-parallel box spanned by the honest updates---carries an unavoidable worst-case cost: every box-valid rule has approximation ratio at least about $\sqrt{\min\{(n-t)/t, d\}}$ (the paper proves $\sqrt{\tfrac{1}{2}\min\{\lfloor (n-t)/t\rfloor, d\}}$). The paper also settles the convex-validity setting by giving a $2d$-approximation algorithm that matches an existing $2d$ lower bound, and reanalyzes the $n

What carries the argument

The central object is the centroid-approximation ratio, built from the smallest ball containing all candidate centroids $\mathrm{SCent}$---the averages of every subset of $n-t$ of the $n$ input vectors---whose radius is called $\mathrm{Rad}_{\mathrm{cov}}$. The proof machinery is the trimmed trusted hyperbox (TTH): with up to $t$ Byzantine reports per coordinate, any box-valid rule must output inside the interval left after removing the $t$ largest and $t$ smallest values in each coordinate. The lower bound collapses the TTH to a single point while the honest centroid sits away from that point. The convex-validity upper bound projects all input vectors onto the line between the safe area (the intersection of the convex hulls of every subset of $n-t$ vectors) and the covering ball, then bounds the number of projected vectors on each side of a separating hyperplane via Lemma 3.13.

What would settle it

To test the box-validity lower bound, instantiate the Lemma 3.11 construction for $n=6$, $t=2$, $d=2$ with $x=1$, enumerate all candidate centroids, and compute the exact minimum covering radius; the ratio of the origin-to-centroid distance to that radius must be at least $1$, and a box-valid rule that beats that ratio on this instance would refute the lower bound. To test the convex-validity claim, search small dimensions for a configuration where a hyperplane touching the safe area leaves more than $q\cdot t$ vectors on the other side; one such configuration would invalidate Lemma 3.13 and the $2d$ upper bound.

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Extended reading notes

Core claim

On its own terms, the paper establishes an almost-tight tradeoff between Byzantine safety and accuracy. The lower-bound construction places $t$ client vectors on each of $k=\min\{\lfloor (n-t)/t\rfloor, d\}$ coordinate axes and the remaining vectors at the origin, then lets the Byzantine clients report the origin; since Byzantine reports are indistinguishable from honest ones, any box-valid rule is forced to output the origin. The honest centroid lies about $\sqrt{k}\cdot \frac{tx}{n-t}$ away, while the minimum covering radius of the candidate centroids is at most $\sqrt{2}\cdot \frac{tx}{n-t}$, giving the ratio $\sqrt{k/2}$. The paper complements this with a $2\sqrt{\min\{n,d\}}$ upper bound for box-valid rules, using the Box and RB-TM algorithms with a new analysis for $n<d$, and a $2d$-approximation algorithm for convex validity, matching the known $2d$ lower bound. It then shows that all these bounds transfer to fully connected peer-to-peer networks by running an exact Byzantine agreement step before applying the aggregation rule.

Load-bearing premise

The convex-validity upper bound rests on Lemma 3.13's claim that a hyperplane touching a $q$-dimensional safe area leaves at most $q\cdot t$ input vectors on its far side; the paper's proof counts $q$ faces at a vertex without fully accounting for vectors that lie on several faces, so the $2d$ approximation collapses if that count is wrong.

Editorial extensions

If this is right

  • Any box-valid aggregation rule, no matter how clever, has worst-case centroid approximation at least about $\sqrt{\min\{(n-t)/t, d\}}$; in high-dimensional models this grows as $\sqrt{d}$.
  • The box-validity gap is almost closed: the upper bound is $2\sqrt{\min\{n,d\}}$, leaving only the constant and the precise $n<d$ behavior open.
  • For convex validity, the existing $2d$ lower bound is tight when $n>(d+1)t$: the safe-area projection algorithm achieves $2d$, settling that regime.
  • Weak and strong validity guarantee only constant approximation ($1$ and $2$ respectively), while convex validity alone gives no bounded guarantee without the safe-area algorithm.
  • All bounds carry over to synchronous peer-to-peer federated learning, because an interactive-consistency round lets every client agree on the same set of vectors before aggregating.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The $\sqrt{d}$ floor suggests that any Byzantine-tolerant averaging scheme that insists on staying coordinate-wise within honest reports will degrade with model size; if outlier robustness is the priority, a weaker validity condition or a rule allowed to step outside the trusted box is worth exploring.
  • The box-validity lower bound only needs Byzantine clients to report the all-zero vector, the same value as some honest clients, so the bound is independent of how sophisticated the Byzantine attack is and likely survives even if Byzantine reports are audited after the fact.
  • One could test the convex-validity algorithm's constant empirically in the regime $n>(d+1)t$, which is unusual for federated learning; the paper's own experiments do not implement it because their models have $d=200$ dimensions.
  • The $2\sqrt{\min\{n,d\}}$ box-validity upper bound may be improvable to $\sqrt{\min\{n,d\}}$ in the $n<d$ case, since the lower-bound construction realizes only about half that value there and the proof's averaging argument leaves room for a tighter constant.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

6 major / 5 minor

Summary. The paper studies aggregation for Byzantine federated learning and evaluates aggregators by the 'centroid approximation' ratio from Cambus and Melnyk [9]: the distance from the aggregator output to the centroid of the non-faulty vectors divided by the radius of the smallest ball covering all centroids of subsets of size n−t. The authors analyze which distributed-computing validity conditions imply a bounded ratio, claim a lower bound min{(n−t)/t,√d} for box validity, an upper bound 2√min{n,d}, and a 2d-approximation algorithm under convex validity that would match a known lower bound. They also claim that the bounds transfer to peer-to-peer networks and present FedSGD/FedAvg experiments. The paper is clearly written, but the main lower-bound claim is not supported by the proofs and is contradicted by the paper's own upper bound.

Significance. The conceptual framing is useful: measuring aggregation quality relative to the input-dependent covering-ball radius is a sensible way to separate Byzantine effects from data heterogeneity, and the experiments illustrate the behavior of the Center-of-ball, MDA, and Box algorithms. If the box-validity lower bound and the convex-validity upper bound were correct, they would be valuable first tightness results. However, the abstract's advertised lower bound min{(n−t)/t,√d} is false: the proof of Lemma 3.11 yields only a square-root expression, and the exact evaluation of that construction gives q/√(q−1)≈√q, not q. Lemma 3.12's convex upper bound is also not proven as stated, since the proof concludes 2d+1 and relies on an unproven counting lemma. The paper does not provide machine-checked proofs or code, and the correctness of the central claims is not established.

major comments (6)
  1. [Abstract, Table 1, Lemma 3.11] The advertised lower bound min{(n−t)/t,√d} is unsupported and contradicted by the paper itself. Lemma 3.11 proves only √(1/2·min{⌊(n−t)/t⌋,d}), which is roughly min{√((n−t)/(2t)),√(d/2)}, not min{(n−t)/t,√d}. For n=6, t=1, d=100 the abstract's bound is 5, while Lemma 3.9 gives an upper bound of 2√6≈4.90. Moreover, in the construction of Lemma 3.11 with q=min{⌊(n−t)/t⌋,d}, the trimmed trusted hyperbox is the single point 0, so every box-valid algorithm must output 0; for n=6, t=1, q=5, the candidate centroids are aΣe_k and aΣ_{k≠j}e_k, whose covering ball has radius a√((q−1)/q), giving an exact ratio of 5/2=2.5. Thus this construction cannot yield a lower bound of 5. The square-root lower bound may be salvageable, but the claimed min{(n−t)/t,√d} bound is false as stated.
  2. [Section 3.1, Lemma 3.4] The proof derives |CH[k]| ≥ (t/(n−t))|TTH[k]|, which implies |TTH[k]| ≤ ((n−t)/t)|CH[k]|, the opposite of the 'TTH diagonal at most t/(n−t) times CH diagonal' used in the next paragraph. The stated worst-case bound (1+t/(n−t))2√d is false: for n=6, t=1, d=1, take non-faulty inputs {0,0,0,100,100} and Byzantine input 0; the algorithm that always outputs the lower endpoint of the trimmed trusted hyperbox is box-valid and outputs 0, while Cent⋆=40 and Radcov=10, so the ratio is 4, exceeding (1+1/5)·2=2.4. The claim that box validity alone guarantees a bounded approximation may still be true via Lemma 3.9, but this lemma's proof and statement need correction.
  3. [Section 3.2, Lemma 3.12 and Lemma 3.13] The upper-bound proof for convex validity is incomplete. The chain at the end gives x/Radcov+1 ≤ 2(n−t−l)/t+1 ≤ 2dt/t+1 = 2d+1, but the lemma claims a 2d-approximation. The missing factor is not a typo, because the only bound on l comes from Lemma 3.13, whose proof is a sketch that sums 'at most t vectors' over q faces without correcting for vectors that lie outside several faces; the claimed 'at most qt points' is therefore not established. Since this is the only argument for tightness of the known convex lower bound, the 2d upper bound is unproven as stated.
  4. [Section 3.2, proof of Lemma 3.11] The displayed norm of the difference between the two centroids is incorrect; the vector is (tx/(n−t))(−e_1+e_q), whose Euclidean norm is √2·tx/(n−t), not 2·√((tx/(n−t))^2). With the corrected value, the lemma's stated lower bound √(q/2) is consistent, so this is a proof error rather than the source of the false abstract claim, but it must be fixed.
  5. [Section 3.2, Lemma 3.9] The new analysis for n<d does not prove the claimed 2√n upper bound. From the fact that Conv(SCent) touches all 2d′ faces of its minimal hyperbox, the proof selects centroids on the d′ faces containing the origin and infers that some centroid lies in the intersection of at least d′/n faces; it then concludes Radcov ≥ √(d′/n)/2. Touching a face only places a point at distance √k/2 from the hyperbox center, and without a second point far from it this does not lower-bound the radius of the minimum covering ball. A rigorous argument for the n<d case is missing.
  6. [Section 3.2, Lemma 3.8] The extension of the 2d lower bound from [9] to all n>(d+1)t is only a sketch; the claims that the non-faulty centroid is at distance td/(n−t) and the covering radius is t/(2(n−t)) are not derived and appear to confuse t√d/(n−t) with td/(n−t). Since this lemma is the matching lower bound for Lemma 3.12, it needs a complete proof.
minor comments (5)
  1. [Table 1] The box-validity lower-bound cells should be updated to the floor and square-root form actually proved in Lemma 3.11; currently they repeat the unsupported min{(n−t)/t,√d} form.
  2. [Lemma 3.13 proof] The notation is inconsistent: the text says 'exactly q (q−1)-faces ... denoted H1,...,Hd' and 'go through sd'; these should be q hyperplanes H1,...,Hq and the vertex s_v.
  3. [Lemma 3.11 construction] The description of the adversarial layout is ambiguous: 't vectors are at coordinate e_k = x·u_k, ∀k∈[...]' should say that for each of the q axes there are t non-faulty vectors at x·u_k and the remaining n−t−qt non-faulty vectors are at the origin.
  4. [Definition 2.7 and Lemma 3.10] The model allows m received messages with n−t≤m≤n, but Lemma 3.4 and Lemma 3.11 silently take m=n; the proofs should state which case they cover.
  5. [Section 4] The experimental section reports single runs without standard deviations or multiple seeds, so statements such as 'MDA shows more instability' and 'Box algorithm appears to be more stable' are not supported quantitatively; also, the Figure 3c caption contains a typo ('cnon-faulty').

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the new bounds are derived from explicit constructions and distance arguments, with prior-work citations used as external building blocks rather than as restatements of the conclusions being proved.

full rationale

The derivation chain in this paper is not circular. The paper inherits the centroid-approximation metric and several building blocks from the authors' earlier work [9], including Definitions 2.2-2.4, the box-validity output condition inside CH and TTH, and the convex-validity lower bound for the special case n=(d+1)t. Those citations are to previously stated results or construction facts, not to the new claims being derived; relying on a prior lemma is not the same as assuming the target theorem. The new box-validity lower bound (Lemma 3.11) is proved by a concrete input layout and uses Lemma 3.10, which is proved in the paper, to force the output of any box-valid algorithm; it does not assume the desired lower bound. The new convex-validity upper bound (Lemma 3.12) is an independent proof that bounds x and Radcov from the geometry of safe area and projections; its main weakness is that Lemma 3.13 is only a sketch and may overcount vectors shared among faces, but that is a support/correctness risk, not circularity. There are no fitted parameters renamed as predictions, and no step reduces by definition to the statement it is supposed to establish. The apparent contradiction between the abstract's advertised min{(n-t)/t, sqrt(d)} lower bound and Lemma 3.11's actual sqrt(min{floor((n-t)/t), d}/2), together with the suspicious norm computation in Lemma 3.11, are arithmetic or statement-level issues that should be raised as correctness concerns, but they do not make the derivation circular.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The theory introduces no numerical free parameters: the bounds are parameter-free expressions in n, t, and d. It relies on standard Byzantine fault-model assumptions, the centroid approximation metric inherited from the authors' prior work [9], and background results on the safe area from Mendes et al. [39]. No new physical or conceptual entities are posited.

assumptions (4)
  • domain assumption Up to t < n/3 clients can be Byzantine and are undetectable as long as they follow the protocol.
    Standard Byzantine fault model introduced in Section 2 and used throughout the paper.
  • domain assumption The centroid approximation metric from [9] is the right measure of aggregation quality, and the worst case assumes exactly t Byzantine vectors.
    Defined in Section 2.1; all bounds are relative to this metric and to the worst-case subset size n-t.
  • domain assumption The safe area for convex validity exists and satisfies the properties from Mendes et al. [39] when n > max{3, d+1} t.
    Used in Lemma 3.12 and Lemma 3.13; cited from [39] and [9].
  • standard math Conv(SCent) spans at most n dimensions and the minimal enclosing coordinate-parallel hyperbox must touch all 2d' faces.
    Used in Lemma 3.9 proof for the n < d case; a geometric fact about minimal enclosing boxes.

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Cite this review

Pith. "Pith review of Centroid Approximation for Byzantine-Tolerant Federated Learning." pith.science (2026). https://pith.science/paper/S56T3FRX

@misc{pith2026250615264,
  author       = {Pith},
  title        = {Pith review of: Centroid Approximation for Byzantine-Tolerant Federated Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/S56T3FRX}},
  note         = {Machine review of arXiv:2506.15264}
}
abstract

Federated learning allows each client to keep its data locally when training machine learning models in a distributed setting. Significant recent research established the requirements that the input must satisfy in order to guarantee convergence of the training loop. This line of work uses averaging as the aggregation rule for the training models. In particular, we are interested in whether federated learning is robust to Byzantine behavior, and observe and investigate a tradeoff between the average/centroid and the validity conditions from distributed computing. We show that the various validity conditions alone do not guarantee a good approximation of the average. Furthermore, we show that reaching good approximation does not give good results in experimental settings due to possible Byzantine outliers. Our main contribution is the first lower bound of $\min\{\frac{n-t}{t},\sqrt{d}\}$ on the centroid approximation under box validity that is often considered in the literature, where $n$ is the number of clients, $t$ the upper bound on the number of Byzantine faults, and $d$ is the dimension of the machine learning model. We complement this lower bound by an upper bound of $2\min\{n,\sqrt{d}\}$, by providing a new analysis for the case $n<d$. In addition, we present a new algorithm that achieves a $\sqrt{2d}$-approximation under convex validity, which also proves that the existing lower bound in the literature is tight. We show that all presented bounds can also be achieved in the distributed peer-to-peer setting. We complement our analytical results with empirical evaluations in federated stochastic gradient descent and federated averaging settings.

Figures

Figures reproduced from arXiv: 2506.15264 by the authors.

Figure 1
Figure 1. Illustration of the benefits of the approximation definition that is relative to the input distribution. This figure shows how the radius of the smallest ball containing all averages depends on different distributions of the inputs. There are 6 clients, one of which is possibly Byzantine. On the left, three input scenarios are considered. The points represent input vectors that are fixed in all scenarios. The three … view at source ↗
Figure 2
Figure 2. FedSGD setting on homogeneous data with MDA, Box and Ballcov(SCent) algorithm (a) FedSGD with mild heterogeneous data. (b) FedSGD with extreme heterogeneous data. (c) Radius of the ball and diameter of non-faulty vectors with mild heterogeneous data distribution in FedSGD setting with f = 1. (d) Radius of the ball and diameter of non-faulty vectors with extreme heterogeneous data distribution in FedSGD setting with … view at source ↗
Figure 3
Figure 3. FedSGD with mild heterogeneous and extreme heterogeneous data under sign flip attack. Figure 2a illustrates the Center of Ballcov(SCent) algorithm in the FedSGD setting with no Byzantine behavior. It can be observed that after 40,000 rounds Ballcov(SCent) algorithm reaches over 77%. The Center of Ballcov(SCent) algorithm requires significantly more rounds than the MDA or the Box algorithm in Figure 2b and is therefo… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FedAvg setting with homogeneous data distributions with and without Byzantine behavior and different heterogeneity distributions. In Figure 2b we evaluate MDA and Box algorithm in the FedSGD setting with homogeneous data distribution under the sign flip attack. We set …

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Works this paper leans on

57 extracted references · 49 canonical work pages

  1. [9]

    Cambus and D

    M. Cambus and D. Melnyk. Improved solutions for multidimensional approximate agreement via centroid computation, 2023. URL https://arxiv.org/abs/2306.12741

    arXiv 2023

  2. [1]

    Journal of Privacy and Confidentiality , 4, 03 2013

    Consumer data privacy in a networked world: A framework for protecting privacy and promoting innovation in the global digital economy. Journal of Privacy and Confidentiality , 4, 03 2013. doi: 10.29012/jpc.v4i2.623

    work page doi:10.29012/jpc.v4i2.623 2013

  3. [2]

    Abbas, M

    W. Abbas, M. Shabbir, J. Li, and X. Koutsoukos. Resilient distributed vector consensus using centerpoint. Automatica, 136:110046, 2022. ISSN 0005-1098

    work page 2022

  4. [3]

    Alistarh, Z

    D. Alistarh, Z. Allen-Zhu, and J. Li. Byzantine stochastic gradient descent. In Advances in Neural Information Processing Systems, volume 31. Curran Associates, Inc., 2018

    work page 2018

  5. [4]

    Bar-Noy and D

    A. Bar-Noy and D. Dolev. Families of consensus algorithms. In VLSI Algorithms and Architectures, 1988. ISBN 978-0-387-34770-7

    work page 1988

  6. [5]

    Bernstein, J

    J. Bernstein, J. Zhao, K. Azizzadenesheli, and A. Anandkumar. signsgd with majority vote is communication efficient and fault tolerant. In 7th International Conference on Learning Representations, ICLR 2019, New Orleans, LA, USA, May 6-9, 2019 . OpenReview.net, 2019

    work page 2019

  7. [6]

    Biggio, B

    B. Biggio, B. Nelson, and P. Laskov. Poisoning attacks against support vector machines. In Proceedings of the 29th International Coference on International Conference on Machine Learning, ICML’12, Madison, WI, USA, 2012

    work page 2012

  8. [7]

    G. Bracha. Asynchronous Byzantine Agreement Protocols. Information and Computation , 75(2):130–143, 1987

    work page 1987

Show all 57 references
  1. [8]

    Bracha and S

    G. Bracha and S. Toueg. Resilient consensus protocols. In Proceedings of the Second Annual ACM Symposium on Principles of Distributed Computing , PODC ’83, 1983. doi: 10.1145/800221.806706

    1983

  2. [10]

    J. Chen, R. Monga, S. Bengio, and R. Jozefowicz. Revisiting distributed synchronous sgd. In International Conference on Learning Representations Workshop Track , 2016. URL https://arxiv.org/abs/1604.00981

    2016 arXiv

  3. [11]

    Civit, S

    P. Civit, S. Gilbert, and V. Gramoli. Polygraph: Accountable byzantine agreement. In 2021 IEEE 41st International Conference on Distributed Computing Systems (ICDCS) , pages 403–413. IEEE, 2021

    2021

  4. [12]

    Civit, M

    P. Civit, M. A. Dzulfikar, S. Gilbert, V. Gramoli, R. Guerraoui, J. Komatovic, and M. Vidigueira. Byzantine consensus is θ (n2): The dolev-reischuk bound is tight even in partial synchrony! In 36th International Symposium on Distributed Computing (DISC 2022). Schloss Dagstuhl-...

    2022

  5. [13]

    Damaskinos, E

    G. Damaskinos, E. M. El Mhamdi, R. Guerraoui, R. Patra, and M. Taziki. Asynchronous Byzantine machine learning (the case of SGD). In Proceedings of the 35th International Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pages 1145–1154. PM...

    2018

  6. [14]

    Data and S

    D. Data and S. Diggavi. Byzantine-resilient high-dimensional sgd with local iterations on heterogeneous data. In International Conference on Machine Learning , pages 2478–2488. PMLR, 2021

    2021

  7. [15]

    J. Dean, G. Corrado, R. Monga, K. Chen, M. Devin, M. Mao, M. a. Ranzato, A. Se- nior, P. Tucker, K. Yang, Q. Le, and A. Ng. Large scale distributed deep networks. In Advances in Neural Information Processing Systems , volume 25. Curran Associates, Inc., 2012. URL https://proce...

    2012

  8. [16]

    Dolev, N

    D. Dolev, N. A. Lynch, S. S. Pinter, E. W. Stark, and W. E. Weihl. Reaching approximate agreement in the presence of faults. J. ACM, 33(3):499–516, May 1986. doi: 10.1145/5925. 5931

    1986 doi

  9. [17]

    E. M. El Mhamdi, R. Guerraoui, and S. Rouault. The hidden vulnerability of distributed learning in Byzantium. In Proceedings of the 35th International Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pages 3521–3530. PMLR, 10–15 Jul 2018

    2018

  10. [18]

    El-Mhamdi, R

    E.-M. El-Mhamdi, R. Guerraoui, A. Guirguis, L. N. Hoang, and S. Rouault. Genuinely distributed byzantine machine learning. In Proceedings of the 39th Symposium on Principles of Distributed Computing , PODC ’20, 2020

    2020

  11. [19]

    E. M. El-Mhamdi, S. Farhadkhani, R. Guerraoui, A. Guirguis, L.-N. Hoang, and S. Rouault. Collaborative learning in the jungle (decentralized, byzantine, heterogeneous, asynchronous and nonconvex learning). Advances in neural information processing systems, 34:25044–25057, 2021

    2021

  12. [20]

    C. Fang, Z. Yang, and W. U. Bajwa. Bridge: Byzantine-resilient decentralized gradient descent. IEEE Transactions on Signal and Information Processing over Networks , 8:610–626, 2022

    2022

  13. [21]

    Farhadkhani, R

    S. Farhadkhani, R. Guerraoui, N. Gupta, R. Pinot, and J. Stephan. Byzantine machine learning made easy by resilient averaging of momentums. In International Conference on Machine Learning, pages 6246–6283. PMLR, 2022

    2022

  14. [22]

    Farhadkhani, R

    S. Farhadkhani, R. Guerraoui, N. Gupta, and R. Pinot. Brief announcement: A case for byzantine machine learning. In Proceedings of the 43rd ACM Symposium on Principles of Distributed Computing, PODC ’24, pages 131–134, 2024

    2024

  15. [23]

    M. J. Fischer and N. A. Lynch. A lower bound for the time to assure interactive consistency. Information Processing Letters, 14(4):183–186, 1982. ISSN 0020-0190

    1982

  16. [24]

    Ghosh, J

    A. Ghosh, J. Hong, D. Yin, and K. Ramchandran. Robust federated learning in a heteroge- neous environment, 2019. URL https://arxiv.org/abs/1906.06629

    2019 arXiv

  17. [25]

    Jee Cho, J

    Y. Jee Cho, J. Wang, and G. Joshi. Towards understanding biased client selection in federated learning. In Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, volume 151 of Proceedings of Machine Learning Research. PMLR, 2022

    2022

  18. [26]

    Jhunjhunwala, P

    D. Jhunjhunwala, P. Sharma, A. Nagarkatti, and G. Joshi. Fedvarp: Tackling the variance due to partial client participation in federated learning. In Uncertainty in Artificial Intelligence , pages 906–916. PMLR, 2022

    2022

  19. [27]

    Jhunjhunwala, S

    D. Jhunjhunwala, S. Wang, and G. Joshi. Fedexp: Speeding up federated averaging via extrapolation. In The Eleventh International Conference on Learning Representations , 2023. 16

    2023

  20. [28]

    R. Jin, Y. Huang, X. He, H. Dai, and T. Wu. Stochastic-sign sgd for federated learning with theoretical guarantees. arXiv preprint arXiv:2002.10940 , 2020

    2002 arXiv

  21. [29]

    Kairouz, H

    P. Kairouz, H. B. McMahan, B. Avent, A. Bellet, M. Bennis, A. N. Bhagoji, K. Bonawitz, Z. Charles, G. Cormode, R. Cummings, et al. Advances and open problems in federated learning. Foundations and trends® in machine learning , 14(1–2):1–210, 2021

    2021

  22. [30]

    S. P. Karimireddy, S. Kale, M. Mohri, S. Reddi, S. Stich, and A. T. Suresh. SCAFFOLD: Stochastic controlled averaging for federated learning. InProceedings of the 37th International Conference on Machine Learning, volume 119 of Proceedings of Machine Learning Research. PMLR, 2020

    2020

  23. [31]

    L. Li, W. Xu, T. Chen, G. B. Giannakis, and Q. Ling. Rsa: Byzantine-robust stochastic aggregation methods for distributed learning from heterogeneous datasets. AAAI’19/IAAI’19/EAAI’19. AAAI Press, 2019. ISBN 978-1-57735-809-1

    2019

  24. [32]

    M. Li, D. G. Andersen, J. W. Park, A. J. Smola, A. Ahmed, V. Josifovski, J. Long, E. J. Shekita, and B.-Y. Su. Scaling distributed machine learning with the parameter server. In Proceedings of the 11th USENIX Conference on Operating Systems Design and Implementation , OSDI’14,...

    2014

  25. [33]

    M. Li, D. G. Andersen, A. J. Smola, and K. Yu. Communication efficient distributed machine learning with the parameter server. In Advances in Neural Information Processing Systems, volume 27. Curran Associates, Inc., 2014

    2014

  26. [34]

    T. Li, A. K. Sahu, M. Zaheer, M. Sanjabi, A. Talwalkar, and V. Smith. Federated optimization in heterogeneous networks. Proceedings of Machine learning and systems , 2:429–450, 2020

    2020

  27. [35]

    Mahloujifar, M

    S. Mahloujifar, M. Mahmoody, and A. Mohammed. Data poisoning attacks in multi-party learning. In ICML, pages 4274–4283, 2019

    2019

  28. [36]

    McMahan, E

    B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. y. Arcas. Communication- Efficient Learning of Deep Networks from Decentralized Data. In Proceedings of the 20th International Conference on Artificial Intelligence and Statistics , volume 54 of Proceedings of Machine Lear...

    2017

  29. [37]

    H. B. McMahan, E. Moore, D. Ramage, and B. A. y Arcas. Federated learning of deep networks using model averaging. arXiv preprint arXiv:1602.05629 , 2(2), 2016

    2016 arXiv

  30. [38]

    Melnyk and R

    D. Melnyk and R. Wattenhofer. Byzantine agreement with interval validity. In 2018 IEEE 37th Symposium on Reliable Distributed Systems (SRDS) , pages 251–260, 2018. doi: 10.1109/SRDS.2018.00036

    2018

  31. [39]

    Mendes, M

    H. Mendes, M. Herlihy, N. Vaidya, and V. K. Garg. Multidimensional agreement in byzantine systems. Distrib. Comput., 28(6), 2015. ISSN 0178-2770

    2015

  32. [40]

    Mitra, R

    A. Mitra, R. Jaafar, G. J. Pappas, and H. Hassani. Linear convergence in federated learning: Tackling client heterogeneity and sparse gradients. In Advances in Neural Information Processing Systems, 2021

    2021

  33. [41]

    Pease, R

    M. Pease, R. Shostak, and L. Lamport. Reaching agreement in the presence of faults. J. ACM, 27(2), Apr. 1980. 17

    1980

  34. [42]

    S. J. Reddi, Z. Charles, M. Zaheer, Z. Garrett, K. Rush, J. Koneˇ cn´ y, S. Kumar, and H. B. McMahan. Adaptive federated optimization. In International Conference on Learning Representations, 2021

    2021

  35. [43]

    Shamir, N

    O. Shamir, N. Srebro, and T. Zhang. Communication-efficient distributed optimization using an approximate newton-type method. In Proceedings of the 31st International Conference on Machine Learning, number 2 in Proceedings of Machine Learning Research, pages 1000–1008, Bejing,...

    2014

  36. [44]

    Sharma and N

    A. Sharma and N. Marchang. Probabilistic sign flipping attack in federated learning. In 2024 15th International Conference on Computing Communication and Networking Technologies (ICCCNT), 2024

    2024

  37. [45]

    J. Shi, W. Wan, S. Hu, J. Lu, and L. Y. Zhang. Challenges and approaches for mitigating byzantine attacks in federated learning. In 2022 IEEE International Conference on Trust, Security and Privacy in Computing and Communications (TrustCom) , pages 139–146. IEEE, 2022

    2022

  38. [46]

    J. So, B. G¨ uler, and A. S. Avestimehr. Byzantine-resilient secure federated learning. IEEE Journal on Selected Areas in Communications , 39(7), 2021

    2021

  39. [47]

    J. Wang, Q. Liu, H. Liang, G. Joshi, and H. V. Poor. Tackling the objective inconsistency problem in heterogeneous federated optimization. NIPS ’20, Red Hook, NY, USA, 2020. Curran Associates Inc. ISBN 9781713829546

    2020

  40. [48]

    X. Wang, S. Mou, and S. Sundaram. A resilient convex combination for consensus-based distributed algorithms. Numerical Algebra, Control and Optimization , 9(3):269–281, 2019. ISSN 2155-3289

    2019

  41. [49]

    Y. Wang, Y. Xia, and Y. Zhan. Elite: Defending federated learning against byzantine attacks based on information entropy. In 2021 China Automation Congress (CAC) , pages 6049–6054, 2021

    2021

  42. [50]

    Z. Wu, Q. Ling, T. Chen, and G. B. Giannakis. Federated variance-reduced stochastic gradient descent with robustness to byzantine attacks. IEEE Transactions on Signal Processing, 68:4583–4596, 2020

    2020

  43. [51]

    C. Xie, S. Koyejo, and I. Gupta. Zeno: Distributed stochastic gradient descent with suspicion-based fault-tolerance. In Proceedings of the 36th International Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research, pages 6893–6901. PMLR, 09–15 Jun 2019

    2019

  44. [52]

    Xu, S.-L

    J. Xu, S.-L. Huang, L. Song, and T. Lan. Byzantine-robust federated learning through collaborative malicious gradient filtering. In 2022 IEEE 42nd International Conference on Distributed Computing Systems (ICDCS) , pages 1223–1235, 2022

    2022

  45. [53]

    Yang and W

    Z. Yang and W. U. Bajwa. Byrdie: Byzantine-resilient distributed coordinate descent for decentralized learning. IEEE Transactions on Signal and Information Processing over Networks, 5(4):611–627, Dec. 2019. ISSN 2373-7778

    2019

  46. [54]

    M. Yin, D. Malkhi, M. K. Reiter, G. G. Gueta, and I. Abraham. Hotstuff: Bft consensus with linearity and responsiveness. In Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing , pages 347–356, 2019

    2019

  47. [55]

    Zhang, Y

    C. Zhang, Y. Xie, H. Bai, B. Yu, W. Li, and Y. Gao. A survey on federated learning. Knowledge-Based Systems, 216:106775, 2021. ISSN 0950-7051. 18

    2021

  48. [56]

    Zhang, J

    Y. Zhang, J. Duchi, M. I. Jordan, and M. J. Wainwright. Information-theoretic lower bounds for distributed statistical estimation with communication constraints. In Advances in Neural Information Processing Systems, volume 26. Curran Associates, Inc., 2013

    2013

  49. [57]

    Y. Zhao, M. Li, L. Lai, N. Suda, D. Civin, and V. Chandra. Federated learning with non-iid data. arXiv preprint arXiv:1806.00582 , 2018. 19

    2018 arXiv

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.