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arxiv: 2604.06430 · v1 · submitted 2026-04-07 · 📡 eess.SY · cs.MA· cs.SY

Asynchronous Distributed Bandit Submodular Maximization under Heterogeneous Communication Delays

Pranjal Sharma , Zirui Xu , Vasileios Tzoumas This is my paper

Pith reviewed 2026-05-10 18:27 UTC · model grok-4.3

classification 📡 eess.SY cs.MAcs.SY
keywords asynchronous distributed optimizationbandit submodular maximizationheterogeneous delaysmulti-agent systemsapproximation boundssensor networksclock mismatches
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The pith

An asynchronous algorithm lets agents maximize submodular objectives with only one-hop messages despite heterogeneous delays and unsynchronized clocks.

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

The paper introduces a coordination algorithm for multiple agents performing bandit submodular maximization in a distributed manner. Each agent communicates only with its immediate neighbors, without assuming simultaneous message arrival or a shared global clock. The central result is a provable bound on how much worse the distributed solution performs compared to an ideal centralized one, with the gap growing explicitly with larger delays, bigger clock mismatches, and sparser local neighborhoods. This addresses practical challenges in information-gathering tasks where perfect timing is impossible. Simulations on multi-camera monitoring confirm the approach works under realistic delay conditions.

Core claim

We develop an asynchronous coordination algorithm for distributed multi-agent bandit submodular maximization under heterogeneous communication delays and mismatched local clocks. The algorithm achieves a provable approximation guarantee relative to the optimal synchronized centralized solution, with the suboptimality gap depending on the communication delays, clock mismatches, and the topology of each agent's one-hop neighborhood.

What carries the argument

Asynchronous coordination algorithm using one-hop neighborhood messages to handle heterogeneous delays and clock mismatches in bandit submodular maximization.

If this is right

  • The performance bound improves as communication delays decrease or as local neighborhoods become more connected.
  • The method remains effective without requiring a global synchronous clock across all agents.
  • Decision quality degrades in a quantifiable way as clock mismatches increase, allowing designers to predict trade-offs.
  • Scalability is supported for large teams since coordination stays local.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Such bounds could guide the design of communication protocols that prioritize reducing specific delays to improve overall performance.
  • The framework might extend to other distributed optimization problems involving uncertainty, like in robotics or environmental monitoring.
  • Testing with real-world delay distributions beyond simulations could validate the bounds further.
  • Agents might adapt their strategies based on observed local delay patterns to tighten the gap.

Load-bearing premise

That limiting coordination to one-hop neighbors under asynchronous conditions still allows a meaningful performance guarantee relative to the best possible centralized solution.

What would settle it

An empirical test showing that the achieved value falls below the predicted approximation ratio for measured delays, clock differences, and given network topology would disprove the guarantee.

Figures

Figures reproduced from arXiv: 2604.06430 by Pranjal Sharma, Vasileios Tzoumas, Zirui Xu.

Figure 1
Figure 1. Figure 1: Simulation layout and sample snapshot of camera (black [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Coverage over time (mean ±95% CI, n = 20 runs, running average over 50 time steps) for DOG-IU and DOG under increasing maximum one-hop delay d¯ on a 100 × 100 workspace with 16 grid-placed cameras, 8 headings, and 80 clustered targets (8 clusters). The gap widens as delay increases, illustrating the benefit of intermediate updates under more severe communication delays. The approximation performance of DOG… view at source ↗
read the original abstract

We study asynchronous distributed decision-making for scalable multi-agent bandit submodular maximization. We are motivated by distributed information-gathering tasks in unknown environments and under heterogeneous inter-agent communication delays. To enable scalability despite limited communication delays, existing approaches restrict each agent to coordinate only with its one-hop neighbors. But these approaches assume homogeneous communication delays among the agents and a synchronous global clock. In practice, however, delays are heterogeneous, and agents operate with mismatched local clocks. That is, each agent does not receive information from all neighbors at the same time, compromising decision-making. In this paper, we provide an asynchronous coordination algorithm to overcome the challenges. We establish a provable approximation guarantee against the optimal synchronized centralized solution, where the suboptimality gap explicitly depends on communication delays and clock mismatches. The bounds also depend on the topology of each neighborhood, capturing the effect of distributed decision-making via one-hop-neighborhood messages only. We validate the approach through numerical simulations on multi-camera area monitoring.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript studies asynchronous distributed bandit submodular maximization for multi-agent systems under heterogeneous communication delays and mismatched local clocks. It proposes an asynchronous coordination algorithm that restricts communication to one-hop neighbors for scalability and establishes a provable approximation guarantee relative to the optimal synchronized centralized solution. The suboptimality gap is claimed to depend explicitly on the heterogeneous delays, clock mismatches, and neighborhood topology. The approach is validated via numerical simulations on a multi-camera area monitoring task.

Significance. If the stated approximation bounds hold, the work would meaningfully extend submodular maximization to realistic asynchronous distributed settings, where prior methods required homogeneous delays and global synchrony. The explicit dependence of the gap on delays, clock drift, and topology provides actionable design insights for applications such as sensor networks. The combination of bandit feedback with one-hop coordination supports scalability in unknown environments, and the modeling of local clocks and message arrival times is a constructive step toward practical analysis.

minor comments (3)
  1. The abstract and introduction would benefit from an explicit statement of the assumptions placed on the delay distributions and clock drifts (e.g., boundedness, independence) before the main theorem is stated.
  2. In the simulation section, the paper should report the specific delay distributions, number of Monte Carlo runs, and quantitative metrics (e.g., regret curves with confidence intervals) used to illustrate the dependence on heterogeneity.
  3. Notation for local clocks, message arrival times, and the one-hop neighborhood sets should be introduced in a dedicated preliminaries subsection with a table of symbols for readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for reviewing our manuscript on asynchronous distributed bandit submodular maximization under heterogeneous communication delays. The referee summary accurately reflects the paper's focus and contributions. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper introduces an asynchronous one-hop coordination algorithm for bandit submodular maximization under heterogeneous delays and derives an approximation guarantee relative to the optimal synchronized centralized optimum. The suboptimality bound is obtained by explicitly modeling local clocks, message arrival times, and neighborhood topology while retaining standard submodularity arguments; none of the load-bearing steps reduce by construction to fitted parameters, self-definitions, or unverified self-citations. The central result is therefore independent of its inputs and externally falsifiable under the stated assumptions on finite heterogeneous delays.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard domain assumptions from submodular optimization and distributed algorithms; no free parameters, new entities, or ad-hoc axioms are introduced in the abstract description.

axioms (2)
  • domain assumption The objective function is submodular, exhibiting the diminishing returns property.
    Core property required for submodular maximization literature and approximation guarantees.
  • domain assumption Agents receive bandit feedback consisting of noisy observations of the objective value.
    Standard setup for bandit optimization in unknown environments.

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Reference graph

Works this paper leans on

37 extracted references · 37 canonical work pages

  1. [1]

    Bandit submodular maximization for multi-robot coordination in unpredictable and partially observable environments,

    Z. Xu, X. Lin, and V . Tzoumas, “Bandit submodular maximization for multi-robot coordination in unpredictable and partially observable environments,” inRobotics: Science and Systems (RSS), 2023

    work page 2023

  2. [2]

    Decentralized active information acquisition: Theory and application to multi-robot SLAM,

    N. Atanasov, J. Le Ny, K. Daniilidis, and G. J. Pappas, “Decentralized active information acquisition: Theory and application to multi-robot SLAM,” inIEEE Inter. Conf. Rob. Auto. (ICRA), 2015, pp. 4775–4782

    work page 2015

  3. [3]

    Distributed submodular maximization on partition matroids for planning on large sensor networks,

    M. Corah and N. Michael, “Distributed submodular maximization on partition matroids for planning on large sensor networks,” inIEEE Conference on Decision and Control (CDC), 2018, pp. 6792–6799

    work page 2018

  4. [4]

    Near-optimal sensor place- ments in gaussian processes: Theory, efficient algorithms and empirical studies,

    A. Krause, A. Singh, and C. Guestrin, “Near-optimal sensor place- ments in gaussian processes: Theory, efficient algorithms and empirical studies,”Jour. Mach. Learn. Res. (JMLR), vol. 9, pp. 235–284, 2008

    work page 2008

  5. [5]

    Efficient informa- tive sensing using multiple robots,

    A. Singh, A. Krause, C. Guestrin, and W. J. Kaiser, “Efficient informa- tive sensing using multiple robots,”Journal of Artificial Intelligence Research (JAIR), vol. 34, pp. 707–755, 2009

    work page 2009

  6. [6]

    Multi-target visual tracking with aerial robots,

    P. Tokekar, V . Isler, and A. Franchi, “Multi-target visual tracking with aerial robots,” inIEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2014, pp. 3067–3072

    work page 2014

  7. [7]

    Distributed submodular maximization with limited information,

    B. Gharesifard and S. L. Smith, “Distributed submodular maximization with limited information,”IEEE Transactions on Control of Network Systems (TCNS), vol. 5, no. 4, pp. 1635–1645, 2017

    work page 2017

  8. [8]

    The role of information in distributed resource allo- cation,

    J. R. Marden, “The role of information in distributed resource allo- cation,”IEEE Transactions on Control of Network Systems (TCNS), vol. 4, no. 3, pp. 654–664, 2017

    work page 2017

  9. [9]

    The impact of information in distributed submodular maximization,

    D. Grimsman, M. S. Ali, J. P. Hespanha, and J. R. Marden, “The impact of information in distributed submodular maximization,”IEEE Trans. Ctrl. Netw. Sys. (TCNS), vol. 6, no. 4, pp. 1334–1343, 2019

    work page 2019

  10. [10]

    Resilient active information acquisition with teams of robots,

    B. Schlotfeldt, V . Tzoumas, and G. J. Pappas, “Resilient active information acquisition with teams of robots,”IEEE Transactions on Robotics (TRO), vol. 38, no. 1, pp. 244–261, 2021

    work page 2021

  11. [11]

    Jacobi-style iteration for dis- tributed submodular maximization,

    B. Du, K. Qian, C. Claudel, and D. Sun, “Jacobi-style iteration for dis- tributed submodular maximization,”IEEE Transactions on Automatic Control (TAC), vol. 67, no. 9, pp. 4687–4702, 2022

    work page 2022

  12. [12]

    Distributed strategy selection: A submodular set function maximization approach,

    N. Rezazadeh and S. S. Kia, “Distributed strategy selection: A submodular set function maximization approach,”Automatica, vol. 153, p. 111000, 2023

    work page 2023

  13. [13]

    Optimal algorithms for submodular maximization with distributed constraints,

    A. Robey, A. Adibi, B. Schlotfeldt, H. Hassani, and G. J. Pappas, “Optimal algorithms for submodular maximization with distributed constraints,” inLearn. for Dyn. & Cont. (L4DC), 2021, pp. 150–162

    work page 2021

  14. [14]

    Communication- and computation-efficient distributed submodular optimization in robot mesh networks,

    Z. Xu, S. S. Garimella, and V . Tzoumas, “Communication- and computation-efficient distributed submodular optimization in robot mesh networks,”IEEE Transactions on Robotics (TRO), 2025

    work page 2025

  15. [15]

    An analysis of approximations for maximizing submodular set functions–II,

    M. L. Fisher, G. L. Nemhauser, and L. A. Wolsey, “An analysis of approximations for maximizing submodular set functions–II,” in Polyhedral combinatorics, 1978, pp. 73–87

    work page 1978

  16. [16]

    A threshold ofln(n)for approximating set cover,

    U. Feige, “A threshold ofln(n)for approximating set cover,”Journal of the ACM (JACM), vol. 45, no. 4, pp. 634–652, 1998

    work page 1998

  17. [17]

    Distributed re- silient submodular action selection in adversarial environments,

    J. Liu, L. Zhou, P. Tokekar, and R. K. Williams, “Distributed re- silient submodular action selection in adversarial environments,”IEEE Robotics and Automation Letters, vol. 6, no. 3, pp. 5832–5839, 2021

    work page 2021

  18. [18]

    Execution order matters in greedy algorithms with limited information,

    R. Konda, D. Grimsman, and J. R. Marden, “Execution order matters in greedy algorithms with limited information,” inAmerican Control Conference (ACC), 2022, pp. 1305–1310

    work page 2022

  19. [19]

    Submodular function maximization,

    A. Krause and D. Golovin, “Submodular function maximization,” Tractability: Practical Approaches to Hard Problems, vol. 3, 2012

    work page 2012

  20. [20]

    Lattimore and C

    T. Lattimore and C. Szepesvári,Bandit Algorithms. Cambridge University Press, 2020

    work page 2020

  21. [21]

    A gaussian process based method for multiple model tracking,

    M. Sun, M. E. Davies, I. Proudler, and J. R. Hopgood, “A gaussian process based method for multiple model tracking,” inSensor Signal Processing for Defence Conference (SSPD), 2020, pp. 1–5

    work page 2020

  22. [22]

    Online submodular coordination with bounded tracking regret: Theory, algorithm, and applications to multi-robot coordination,

    Z. Xu, H. Zhou, and V . Tzoumas, “Online submodular coordination with bounded tracking regret: Theory, algorithm, and applications to multi-robot coordination,”IEEE Robotics and Automation Letters (RAL), vol. 8, no. 4, pp. 2261–2268, 2023

    work page 2023

  23. [23]

    Explore no more: Improved high-probability regret bounds for non-stochastic bandits,

    G. Neu, “Explore no more: Improved high-probability regret bounds for non-stochastic bandits,”Adv. Neu. Info. Proc. Sys., vol. 28, 2015

    work page 2015

  24. [24]

    Self-configurable mesh-networks for scalable distributed submodular bandit optimization,

    Z. Xu and V . Tzoumas, “Self-configurable mesh-networks for scalable distributed submodular bandit optimization,”arXiv preprint:2602.19366, 2026

    work page arXiv 2026

  25. [25]

    Distributed online submodular maximization under commu- nication delays: A simultaneous decision-making approach,

    ——, “Distributed online submodular maximization under commu- nication delays: A simultaneous decision-making approach,”arXiv preprint:2603.27803, 2026

    work page arXiv 2026

  26. [26]

    Nonstochastic multi- armed bandits with unrestricted delays,

    T. S. Thune, N. Cesa-Bianchi, and Y . Seldin, “Nonstochastic multi- armed bandits with unrestricted delays,”Advances in Neural Informa- tion Processing Systems (NeurIPS), vol. 32, 2019

    work page 2019

  27. [27]

    A characterization of a cone of pseudo-boolean functions via supermodularity-type inequal- ities,

    Y . Crama, P. L. Hammer, and R. Holzman, “A characterization of a cone of pseudo-boolean functions via supermodularity-type inequal- ities,” inQuantitative Methoden in den Wirtschaftswissenschaften. Springer, 1989, pp. 53–55

    work page 1989

  28. [28]

    Submodularity, supermodularity, and higher-order monotonicities of pseudo-boolean functions,

    S. Foldes and P. L. Hammer, “Submodularity, supermodularity, and higher-order monotonicities of pseudo-boolean functions,”Mathemat- ics of Operations Research, vol. 30, no. 2, pp. 453–461, 2005

    work page 2005

  29. [29]

    Submodular set functions, matroids and the greedy algorithm: Tight worst-case bounds and some general- izations of the rado-edmonds theorem,

    M. Conforti and G. Cornuéjols, “Submodular set functions, matroids and the greedy algorithm: Tight worst-case bounds and some general- izations of the rado-edmonds theorem,”Discrete Applied Mathematics, vol. 7, no. 3, pp. 251–274, 1984

    work page 1984

  30. [30]

    Optimal approximation for submodular and supermodular optimization with bounded curvature,

    M. Sviridenko, J. V ondrák, and J. Ward, “Optimal approximation for submodular and supermodular optimization with bounded curvature,” Math. of Operations Research, vol. 42, no. 4, pp. 1197–1218, 2017

    work page 2017

  31. [31]

    Time, clocks, and the ordering of events in a distributed system,

    L. Lamport, “Time, clocks, and the ordering of events in a distributed system,”Communications of the ACM, 1978

    work page 1978

  32. [32]

    Fundamental limits on synchronizing clocks over networks,

    N. M. Freris, S. R. Graham, and P. Kumar, “Fundamental limits on synchronizing clocks over networks,”IEEE Transactions on Automatic Control (TAC), vol. 56, no. 6, pp. 1352–1364, 2010

    work page 2010

  33. [33]

    Distributed asyn- chronous deterministic and stochastic gradient optimization algo- rithms,

    J. N. Tsitsiklis, D. P. Bertsekas, and M. Athans, “Distributed asyn- chronous deterministic and stochastic gradient optimization algo- rithms,”IEEE Transactions on Automatic Control, vol. 31, no. 9, pp. 803–812, 1986

    work page 1986

  34. [34]

    Gradient clock synchronization,

    R. Fan and N. Lynch, “Gradient clock synchronization,” inProceed- ings of the Twenty-Third Annual ACM Symposium on Principles of Distributed Computing, ser. PODC ’04. ACM, 2004, pp. 320–327

    work page 2004

  35. [35]

    Decentralized safe control for distributed cyber-physical systems using real-time reachability analysis,

    L. V . Nguyen, H.-D. Tran, T. T. Johnson, and V . Gupta, “Decentralized safe control for distributed cyber-physical systems using real-time reachability analysis,”IEEE Transactions on Control of Network Systems, vol. 10, no. 3, pp. 1234–1244, 2023

    work page 2023

  36. [36]

    Online learning with predictable sequences,

    A. Rakhlin and K. Sridharan, “Online learning with predictable sequences,” inConference on Learning Theory, 2013, pp. 993–1019

    work page 2013

  37. [37]

    Softmax is1/2-lipschitz: A tight bound across allℓ p norms,

    P. Nair, “Softmax is1/2-lipschitz: A tight bound across allℓ p norms,”Transactions on Machine Learning Research, 2026. [Online]. Available: https://openreview.net/forum?id=6dowaHsa6D APPENDIXI PROOF OFTHEOREM1 We prove the main result by establishing how far offˆpt of DOG-IUis from the reference distributionp Exp3 t correspond- ing to the standardEXP3band...

    work page 2026