Pith. sign in

REVIEW 3 minor 42 references

Decentralized Parameter-Free Online Learning with Compressed Gossip

T0 review · 0 major / 3 minor · reviewed 2026-06-29 · grok-4.3

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read DECO-EF achieves expected sublinear network regret for parameter-free decentralized online convex optimization under compressed communication.

desk verdict The paper claims the first parameter-free sublinear network regret bounds for decentralized online convex optimization under compressed communication via coin-betting plus error-feedback gossip. read the letter →

arxiv 2605.27831 v1 pith:X4LTSSOW submitted 2026-05-27 cs.LG eess.SPmath.OC

Tomas Ortega , Hamid Jafarkhani This is my paper · ORCID
classification cs.LGeess.SPmath.OC
keywords decentralizedonlinelearningcompressedcommunicationparameter-freealgorithmscoinbettingnetworkregreterrorfeedbackgossip
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 introduces DECO-EF, which lets multiple agents on a graph solve online convex optimization by maintaining a clean accumulated state and a compressed tracker while exchanging only compressed state differences during gossip rounds. It combines coin-betting predictions with error feedback to keep the extra disagreement from compression from breaking the regret analysis. The central result is an expected comparator-adaptive network-regret bound that grows sublinearly without any tuning to the time horizon or the comparator norm. A sympathetic reader cares because the method removes the usual requirements for knowing problem parameters in advance and for sending full-precision messages, both of which limit real distributed deployments.

What carries the argument

Compressed difference-based gossip with error feedback, which maintains a clean state and compressed tracker so that coin-betting analysis still controls total network disagreement.

What would settle it

A simulation on a fixed graph with a standard compressor in which the measured cumulative network regret grows linearly with the number of rounds would falsify the sublinear bound.

Watch

Extended reading notes

Core claim

DECO-EF is a decentralized parameter-free online learning algorithm that combines coin-betting predictions with compressed difference-based gossip. Each agent maintains a clean accumulated state and a compressed tracker, and communicates only compressed state differences during gossip steps. The method proves expected comparator-adaptive network-regret bounds under compressed communication and supplies the first such sublinear guarantees for parameter-free decentralized online learning under compressed communication.

Load-bearing premise

The compressed difference-based gossip together with error feedback sufficiently controls the additional disagreement introduced by compression so that the coin-betting analysis still yields sublinear network regret.

Editorial extensions

If this is right

  • Network regret remains sublinear in expectation and scales with the best comparator norm.
  • No tuning to horizon length or learning-rate scale is required.
  • The same regret guarantees hold when messages are compressed rather than transmitted at full precision.
  • The approach applies to any connected communication graph.

Reading between the lines

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

  • The compression technique may extend directly to other coin-betting or parameter-free methods without changing their core analysis.
  • Bandwidth savings could make the algorithm practical on resource-limited networks where full-precision gossip is prohibitive.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 3 minor

Summary. The manuscript proposes DECO-EF, a decentralized parameter-free online convex optimization algorithm that combines coin-betting predictions with compressed difference-based gossip and error feedback. Each agent maintains a clean accumulated state and a compressed tracker, communicating only compressed differences. The central claim is a proof of expected comparator-adaptive network-regret bounds under compressed communication, asserted to be the first such sublinear guarantees for parameter-free decentralized online learning with compression.

Significance. If the regret analysis holds, the result would be significant for bridging parameter-free online learning (via coin-betting) with practical compressed decentralized settings. It extends known techniques for controlling disagreement from compression while preserving comparator-adaptivity and avoiding horizon- or norm-dependent tuning, which is relevant for distributed systems where communication bandwidth is limited.

minor comments (3)
  1. The abstract and introduction should explicitly define 'network-regret' (e.g., sum of local regrets plus a disagreement term) and state the precise assumptions on the communication graph and compression operator before claiming the bounds.
  2. Notation for the error-feedback mechanism and the clean vs. compressed states should be introduced with a clear table or diagram in §3, as the current description risks ambiguity when tracking the additional disagreement term induced by compression.
  3. The manuscript should include a brief comparison table (e.g., Table 1) contrasting DECO-EF regret dependence on T, network size, and compression ratio against prior works such as standard decentralized OCO and compressed gossip methods.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive evaluation of the manuscript. The summary accurately reflects the main contribution of DECO-EF. No specific major comments were raised in the report.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; derivation self-contained

full rationale

The paper introduces the DECO-EF algorithm by combining coin-betting predictions with difference-based compressed gossip plus error feedback, then states a proof of expected comparator-adaptive network-regret bounds. No quoted step reduces a claimed prediction or bound to a fitted parameter, a self-citation chain, or a renamed input by construction. The central result is the existence of the regret analysis under the stated compression control assumption; this is presented as an independent extension rather than a tautology or load-bearing self-reference. The derivation chain therefore remains non-circular on the supplied material.

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

Only abstract available; no free parameters, axioms, or invented entities can be extracted.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Decentralized Parameter-Free Online Learning with Compressed Gossip." pith.science (2026). https://pith.science/paper/X4LTSSOW

@misc{pith2026260527831,
  author       = {Pith},
  title        = {Pith review of: Decentralized Parameter-Free Online Learning with Compressed Gossip},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X4LTSSOW}},
  note         = {Machine review of arXiv:2605.27831}
}
read the original abstract

We study decentralized online convex optimization when agents communicate over a graph and messages may be compressed. Classical decentralized online methods typically require learning-rate choices that depend on the horizon, comparator scale, or other problem parameters, while compressed communication introduces additional disagreement that must be controlled. We propose DECO-EF (DEcentralized COin-betting with Error Feedback), a decentralized parameter-free online learning algorithm that combines coin-betting predictions with compressed difference-based gossip. Each agent maintains a clean accumulated state and a compressed tracker, and communicates only compressed state differences during gossip steps. The method is parameter-free in the online-learning sense: it does not tune to the horizon, the comparator norm, or the learning rate. We prove expected comparator-adaptive network-regret bounds for DECO-EF under compressed communication. To the best of our knowledge, this gives the first expected sublinear network-regret guarantees for parameter-free decentralized online learning under compressed communication.

Figures

Figures reproduced from arXiv: 2605.27831 by the authors.

Figure 1
Figure 1. System model for DECO-EF. Agents make local predictions, [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. LIBSVM online-regression experiments, showing decentralized online gradient descent (DOGD) tuning sensitivity on the ring graph [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Synthetic quantized-communication diagnostics for DECO-EF. All decentralized runs use [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

42 extracted references · 11 canonical work pages

  1. [1]

    Introduction to online convex optimization, 2023

    E. Hazan, “Introduction to Online Convex Optimization,” arXiv, Aug. 2023, arXiv:1909.05207 [cs]

    work page arXiv 2023

  2. [2]

    Online Learning and Online Convex Optimization,

    S. Shalev-Shwartz, “Online Learning and Online Convex Optimization,”Foundations and Trends®in Machine Learning, vol. 4, no. 2, pp. 107–194, 2011

    2011

  3. [3]

    Icml 2020 tutorial on parameter-free online optimization,

    F. Orabona and A. Cutkosky, “Icml 2020 tutorial on parameter-free online optimization,” inWebsites: https://parameterfree.com/icml-tutorial/, https://icml.cc/Conferences/2020/Schedule, 2020

    2020

  4. [4]

    Online Learning: A Modern Introduction Using Convex Optimization

    F. Orabona, “A Modern Introduction to Online Learning,” arXiv, May 2023, arXiv:1912.13213 [cs]

    work page Pith review arXiv 2023

  5. [5]

    No-Regret Algorithms for Unconstrained Online Convex Optimization,

    B. Mcmahan and M. Streeter, “No-Regret Algorithms for Unconstrained Online Convex Optimization,” inAdvances in Neural Information Processing Systems, vol. 25. Curran Associates, Inc., 2012

    2012

  6. [6]

    Unconstrained Online Linear Learning in Hilbert Spaces: Minimax Algorithms and Normal Approximations,

    H. B. McMahan and F. Orabona, “Unconstrained Online Linear Learning in Hilbert Spaces: Minimax Algorithms and Normal Approximations,” inProceedings of The 27th Conference on Learning Theory. PMLR, May 2014, pp. 1020–1039, iSSN: 1938-7228

    2014

  7. [7]

    Coin Betting and Parameter-Free Online Learning

    F. Orabona and D. P´ al, “Coin Betting and Parameter-Free Online Learning,”arXiv, Nov. 2016, arXiv:1602.04128 [cs]. 13

    work page Pith review arXiv 2016

  8. [8]

    Online Convex Optimization with Unconstrained Domains and Losses

    A. Cutkosky and K. Boahen, “Online Convex Optimization with Unconstrained Domains and Losses,”arXiv, Mar. 2017, arXiv:1703.02622 [cs]

    work page Pith review arXiv 2017

Show all 42 references
  1. [9]

    Comparator-adaptive convex bandits,

    D. van der Hoeven, A. Cutkosky, and H. Luo, “Comparator-adaptive convex bandits,” inProceedings of the 34th International Conference on Neural Information Processing Systems, ser. NIPS ’20. Red Hook, NY, USA: Curran Associates Inc., Dec. 2020, pp. 19 795–19 804

    2020

  2. [10]

    Distributed optimization in sensor networks,

    M. Rabbat and R. Nowak, “Distributed optimization in sensor networks,” inThird International Symposium on Information Processing in Sensor Networks, 2004. IPSN 2004, Apr. 2004, pp. 20–27

    2004

  3. [11]

    A simple peer-to-peer algorithm for distributed optimization in sensor networks,

    B. Johansson, M. Rabi, and M. Johansson, “A simple peer-to-peer algorithm for distributed optimization in sensor networks,” in2007 46th IEEE Conference on Decision and Control, Dec. 2007, pp. 4705–4710, iSSN: 0191-2216

    2007

  4. [12]

    On the rate of convergence of distributed subgradient methods for multi-agent optimization,

    A. Nedic and A. Ozdaglar, “On the rate of convergence of distributed subgradient methods for multi-agent optimization,” in2007 46th IEEE Conference on Decision and Control, Dec. 2007, pp. 4711–4716, iSSN: 0191-2216

    2007

  5. [13]

    Distributed Optimization for Control,

    A. Nedi´ c and J. Liu, “Distributed Optimization for Control,” Annual Review of Control, Robotics, and Autonomous Systems, vol. 1, no. 1, pp. 77–103, May 2018

    2018

  6. [14]

    Cooperative online learning: Keeping your neighbors updated,

    N. Cesa-Bianchi, T. Cesari, and C. Monteleoni, “Cooperative online learning: Keeping your neighbors updated,” in Proceedings of the 31st International Conference on Algorithmic Learning Theory. PMLR, Jan. 2020, pp. 234–250

    2020

  7. [15]

    Cooperative online learning with feedback graphs,

    N. Cesa-Bianchi, T. R. Cesari, and R. Della Vecchia, “Cooperative online learning with feedback graphs,”arXiv preprint arXiv:2106.04982, 2021

    2021

  8. [16]

    Distributed Online Optimization with Stochastic Agent Availability,

    J. Achddou, N. Cesa-Bianchi, and H. Qiu, “Distributed Online Optimization with Stochastic Agent Availability,”arXiv, Nov. 2024, arXiv:2411.16477 [cs]

    2024

  9. [17]

    Multi-agent online optimization with delays: asynchronicity, adaptivity, and optimism,

    Y.-G. Hsieh, F. Iutzeler, J. Malick, and P. Mertikopoulos, “Multi-agent online optimization with delays: asynchronicity, adaptivity, and optimism,”J. Mach. Learn. Res., vol. 23, no. 1, pp. 78:3377–78:3425, Jan. 2022

    2022

  10. [18]

    Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling,

    J. C. Duchi, A. Agarwal, and M. J. Wainwright, “Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling,”IEEE Transactions on Automatic Control, vol. 57, no. 3, pp. 592–606, Mar. 2012

    2012

  11. [19]

    Decentralized online optimization with global objectives and local communication,

    A. Nedi´ c, S. Lee, and M. Raginsky, “Decentralized online optimization with global objectives and local communication,” in2015 American Control Conference (ACC), Jul. 2015, pp. 4497–4503, iSSN: 2378-5861

    2015

  12. [20]

    Network Topology and Communication-Computation Tradeoffs in Decentralized Optimization,

    A. Nedi´ c, A. Olshevsky, and M. G. Rabbat, “Network Topology and Communication-Computation Tradeoffs in Decentralized Optimization,”Proceedings of the IEEE, vol. 106, no. 5, pp. 953–976, May 2018

    2018

  13. [21]

    Online distributed optimization via dual averaging,

    S. Hosseini, A. Chapman, and M. Mesbahi, “Online distributed optimization via dual averaging,” in52nd IEEE Conference on Decision and Control, Dec. 2013, pp. 1484–1489, iSSN: 0191-2216

    2013

  14. [22]

    Distributed Online Learning for Joint Regret with Communication Constraints,

    D. v. d. Hoeven, H. Hadiji, and T. v. Erven, “Distributed Online Learning for Joint Regret with Communication Constraints,”arXiv, Oct. 2021, arXiv:2102.07521 [cs]

    2021

  15. [23]

    QSGD: Communication-efficient SGD via gradient quantization and encoding,

    D. Alistarh, D. Grubic, J. Li, R. Tomioka, and M. Vojnovic, “QSGD: Communication-efficient SGD via gradient quantization and encoding,” inAdvances in Neural Information Processing Systems, I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Ferguset al., Eds., vol. 30. Curran A...

    2017

  16. [24]

    Sparsified SGD with memory,

    S. U. Stich, J.-B. Cordonnier, and M. Jaggi, “Sparsified SGD with memory,” inAdvances in Neural Information Processing Systems, vol. 31. Curran Associates, Inc., 2018

    2018

  17. [25]

    Advances and open problems in federated learning,

    P. Kairouz, H. B. McMahan, B. Avent, A. Bellet, M. Bennis et al., “Advances and open problems in federated learning,” Foundations and Trends®in Machine Learning, vol. 14, no. 1-2, pp. 1–210, 2021

    2021

  18. [26]

    Error feedback fixes signSGD and other gradient compression schemes,

    S. P. Karimireddy, Q. Rebjock, S. Stich, and M. Jaggi, “Error feedback fixes signSGD and other gradient compression schemes,” inProceedings of the 36th International Conference on Machine Learning. PMLR, May 2019, pp. 3252–3261

    2019

  19. [27]

    EF21: A new, simpler, theoretically better, and practically faster error feedback,

    P. Richtarik, I. Sokolov, and I. Fatkhullin, “EF21: A new, simpler, theoretically better, and practically faster error feedback,” inAdvances in Neural Information Processing Systems, vol. 34. Curran Associates, Inc., 2021, pp. 4384–4396

    2021

  20. [28]

    A better alternative to error feedback for communication-efficient distributed learning,

    S. Horv´ ath and P. Richtarik, “A better alternative to error feedback for communication-efficient distributed learning,” in International Conference on Learning Representations, 2021

    2021

  21. [29]

    Asynchronous federated learning with bidirectional quantized communications and buffered aggregation,

    T. Ortega and H. Jafarkhani, “Asynchronous federated learning with bidirectional quantized communications and buffered aggregation,”arXiv, no. arXiv:2308.00263, Jul. 2023

    2023

  22. [30]

    Quantized and asynchronous federated learning,

    ——, “Quantized and asynchronous federated learning,”IEEE Transactions on Communications, vol. 73, no. 4, pp. 2361–2374, 2025

    2025

  23. [31]

    Decentralized Stochastic Optimization and Gossip Algorithms with Compressed Communication,

    A. Koloskova, S. Stich, and M. Jaggi, “Decentralized Stochastic Optimization and Gossip Algorithms with Compressed Communication,” inProceedings of the 36th International Conference on Machine Learning. PMLR, May 2019, pp. 3478–3487, iSSN: 2640-3498

    2019

  24. [32]

    Decentralized Deep Learning with Arbitrary Communication Compression,

    A. Koloskova, T. Lin, S. U. Stich, and M. Jaggi, “Decentralized Deep Learning with Arbitrary Communication Compression,” inInternational Conference on Learning Representations, Apr. 2020

    2020

  25. [33]

    Distributed and quantized online multi-kernel learning,

    Y. Shen, S. Karimi-Bidhendi, and H. Jafarkhani, “Distributed and quantized online multi-kernel learning,”IEEE Transactions on Signal Processing, vol. 69, pp. 5496–5511, 2021

    2021

  26. [34]

    Gossiped and quantized online multi-kernel learning,

    T. Ortega and H. Jafarkhani, “Gossiped and quantized online multi-kernel learning,”IEEE Signal Processing Letters, vol. 30, pp. 468–472, 2023

    2023

  27. [35]

    Communication compression for distributed learning without control variates,

    T. Ortega, C.-Y. Huang, X. Li, and H. Jafarkhani, “Communication compression for distributed learning without control variates,”arXiv, no. arXiv:2412.04538, Dec. 2024

    2024

  28. [36]

    Communication compression for distributed learning with aggregate and server-guided feedback,

    ——, “Communication compression for distributed learning with aggregate and server-guided feedback,”arXiv, no. arXiv:2512.22623, 2025

    2025

  29. [37]

    Decentralized parameter-free online learning,

    T. Ortega and H. Jafarkhani, “Decentralized parameter-free online learning,”arXiv, no. arXiv:2510.15644, Oct. 2025

    2025

  30. [38]

    Improved regret for decentralized online convex optimization with compressed communication,

    S. Yang, W. Yang, W. Jiang, and L. Zhang, “Improved regret for decentralized online convex optimization with compressed communication,” Oct. 2025

    2025

  31. [39]

    Decentralized online convex optimization with compressed communications,

    X. Cao and T. Ba¸ sar, “Decentralized online convex optimization with compressed communications,”Automatica, vol. 156, p. 111186, Oct. 2023

    2023

  32. [40]

    Randomized gossip algorithms,

    S. Boyd, A. Ghosh, B. Prabhakar, and D. Shah, “Randomized gossip algorithms,”IEEE Transactions on Information Theory, vol. 52, no. 6, pp. 2508–2530, Jun. 2006

    2006

  33. [41]

    PowerSGD: Practical low-rank gradient compression for distributed optimization,

    T. Vogels, S. P. Karimireddy, and M. Jaggi, “PowerSGD: Practical low-rank gradient compression for distributed optimization,”Advances in Neural Information Processing Systems, vol. 32, 2019

    2019

  34. [42]

    LIBSVM: A library for support vector machines,

    C.-C. Chang and C.-J. Lin, “LIBSVM: A library for support vector machines,”ACM Transactions on Intelligent Systems and Technology, vol. 2, no. 3, pp. 1–27, Apr. 2011

    2011

Pith tools

Reviewed June 29, 2026 · model on record in the stance chip above.