arxiv: 2605.06202 · v1 · submitted 2026-05-07 · 💻 cs.LG · stat.ML

Recognition: unknown

Bandit Learning in General Open Multi-agent Systems

Mengfan Xu

Authors on Pith no claims yet

Pith reviewed 2026-05-08 13:27 UTC · model grok-4.3

classification 💻 cs.LG stat.ML

keywords bandit learningopen systemsmulti-agentdynamic regretglobal-UCBpre-training degreestabilityregret bounds

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The pith

Global-UCB bandit algorithms achieve provable regret in open multi-agent systems with linear scaling in pre-training uncertainty.

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

The paper addresses bandit learning in open systems where agents arrive and depart, creating challenges like non-stationarity from new agents and scaling regret with the time horizon. It defines pre-training degree to capture information new agents bring upon entry, stability to quantify how new agents affect the system, and global dynamic regret to measure performance against changing optimal actions. Certified global-UCB methods are introduced that deliver regret bounds depending linearly on pre-training degree for entry uncertainty, and on identification time plus agent patterns in stable regimes. Lower bounds in hard instances prove these dependencies are tight. This matters for real digital platforms with dynamic user participation, as it allows bounding learning losses without strong assumptions on agent behaviors.

Core claim

We formulate a unified open-system bandit problem with general dynamics including heterogeneous rewards and general agent patterns. New concepts include the pre-training degree quantifying information carried by new agents, stability measuring new agents' system impact, and global dynamic regret comparing active agents' cumulative reward to varying optimal arms. Certified global-UCB methodologies are developed with provable guarantees, revealing linear entry of entry uncertainty via pre-training degree and regret governed by optimal arm identification time and agent patterns in stable regimes, with tightness shown via lower bounds.

What carries the argument

Global-UCB, the upper confidence bound algorithm adapted to global dynamic regret that accounts for pre-training degree and stability to provide certified performance in open systems.

Load-bearing premise

Pre-training degree and stability are well-defined quantities that can be used to derive regret bounds for general agent dynamics without further restrictions.

What would settle it

A simulation or real deployment in an open system where measured regret grows super-linearly with pre-training degree, despite fixed stability and patterns, would falsify the claimed bounds.

read the original abstract

Recent developments in digital platforms have highlighted the prevalence of open systems, where agents can arrive and depart over time. While bandit learning in open systems has recently received initial attention, existing work imposes structural assumptions that are frequently violated in practice. A learning paradigm for general open systems creates fresh challenges: newly arriving agents induce endogenous non-stationarity; agent patterns determine how quickly information accumulates; and new agents make regret scale further with the time horizon. To this end, we formulate a unified open-system bandit problem with general dynamics, including heterogeneous rewards and general agent patterns. We introduce new concepts to capture the inherent complexities: the \emph{pre-training degree} of new agents quantifies how much information an agent carries upon entry, \emph{stability} measures the impact of new agents on the system, and \emph{global dynamic regret} compares the cumulative expected reward of all active agents with that of the varying optimal arms. We develop certified global-UCB learning methodologies with provable guarantees. Our regret bounds reveal that entry uncertainty enters linearly via the pre-training degree, while in stable regimes, regret is governed by the time needed to identify a persistent optimal arm, as well as by the agent patterns. We further show that these dependencies are tight via lower bounds in hard instances.

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.

Desk Editor's Note private letter to a colleague

The paper defines pre-training degree and stability to handle general open multi-agent bandits and gives global-UCB bounds with matching lower bounds, but treats those quantities as known inputs rather than estimated ones.

read the letter

The main point is that this work sets up bandit learning for open systems where agents arrive and depart with no structural restrictions on rewards or patterns. It introduces pre-training degree to measure information new agents carry on entry, stability to capture how arrivals affect the overall system, and global dynamic regret to compare total reward against the best arm available to each active agent at each step. The global-UCB method then produces regret bounds that scale linearly with pre-training degree in the general case and depend on identification time plus agent patterns when the system is stable, with lower bounds shown on hard instances to confirm tightness. That unified formulation without the usual assumptions is the clearest step forward from earlier open-bandit papers. The lower bounds and the focus on endogenous non-stationarity from arrivals are useful additions that match the practical setting of digital platforms. The soft spot is that the bounds appear to plug in pre-training degree and stability directly as parameters. In a fully general heterogeneous setting it is not obvious how an algorithm would observe or estimate them from data alone, and the abstract does not spell out a procedure for doing so. If those quantities cannot be recovered without extra assumptions, the claimed guarantees become conditional in ways that matter for deployment. This is aimed at theorists working on dynamic multi-agent online learning. A reader who wants to see regret analysis extended beyond fixed or restricted open models will find the new concepts and bounds worth examining. It has enough concrete definitions and results to merit sending to referees rather than desk rejection, though any review should check whether the proofs require the new quantities to be known or provide a way to learn them.

Referee Report

2 major / 2 minor

Summary. The paper formulates a unified bandit learning problem in general open multi-agent systems allowing arbitrary agent arrivals/departures, heterogeneous rewards, and general agent patterns. It defines pre-training degree (information carried by new agents upon entry), stability (impact of new agents on the system), and global dynamic regret (cumulative reward of active agents versus varying per-period optima). The authors propose global-UCB algorithms and derive regret bounds in which entry uncertainty enters linearly through pre-training degree, while stable regimes have regret governed by identification time for persistent optima plus agent patterns; matching lower bounds are shown on hard instances.

Significance. If the derivations hold, the work meaningfully extends bandit theory to fully general open systems without the structural assumptions common in prior literature. The explicit dependence of bounds on pre-training degree and stability, together with tightness via lower bounds, offers concrete insight into how agent dynamics affect regret; this could influence analysis of dynamic platforms. No machine-checked proofs or reproducible code are referenced, but the parameter-free character of the linear dependence (if verified) would be a strength.

major comments (2)

[Abstract and §2] Abstract and §2 (new concepts): the central regret bounds treat pre-training degree as a known scalar that enters linearly, yet no procedure is given for recovering or estimating it from observations under fully general heterogeneous rewards and agent patterns. This is load-bearing for the 'provable guarantees' claim, as the skeptic correctly notes that unobservable parameters undermine certification in the general case the paper targets.
[Main regret theorem (likely §4)] Main regret theorem (likely §4): the bound separating stable regimes (regret governed by identification time and agent patterns) from the linear pre-training term assumes stability can be used directly without additional structural assumptions on dynamics. If stability is not observable or estimable from data alone, the separation does not yield practical guarantees, contradicting the paper's emphasis on generality.

minor comments (2)

[§2] Notation for global dynamic regret should include a short illustrative example early in the paper to clarify comparison against time-varying optima.
[Abstract] The abstract states 'certified' methodologies; the manuscript should explicitly list all assumptions (including any implicit observability requirements) in a dedicated paragraph before the theorems.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below with clarifications on the modeling parameters and their role in the theoretical guarantees. We believe these can be resolved by adding discussion to the manuscript.

read point-by-point responses

Referee: [Abstract and §2] Abstract and §2 (new concepts): the central regret bounds treat pre-training degree as a known scalar that enters linearly, yet no procedure is given for recovering or estimating it from observations under fully general heterogeneous rewards and agent patterns. This is load-bearing for the 'provable guarantees' claim, as the skeptic correctly notes that unobservable parameters undermine certification in the general case the paper targets.

Authors: The pre-training degree is introduced as a modeling parameter quantifying information carried by new agents, allowing regret bounds to explicitly capture its linear effect on entry uncertainty. The global-UCB algorithm itself requires no knowledge of this parameter and operates solely on observed rewards from active agents. This mirrors standard bandit analyses where bounds depend on unknown quantities such as gaps. The guarantees are therefore provable conditionally on the model, characterizing worst-case performance under general dynamics. We will add a remark in §2 noting that precise estimation may need application-specific assumptions, but the bounds provide insight into the impact without requiring the parameter for algorithm execution. revision: partial
Referee: [Main regret theorem (likely §4)] Main regret theorem (likely §4): the bound separating stable regimes (regret governed by identification time and agent patterns) from the linear pre-training term assumes stability can be used directly without additional structural assumptions on dynamics. If stability is not observable or estimable from data alone, the separation does not yield practical guarantees, contradicting the paper's emphasis on generality.

Authors: Stability is a modeling concept measuring the impact of new agents, and the regret bound uses it to separate regimes and show that stable systems have regret driven by identification time and agent patterns. The global-UCB algorithm does not require knowledge of stability and uses only empirical observations. The separation is a theoretical tool to characterize performance under varying dynamics, analogous to assumptions in other non-stationary bandit settings. We will revise the discussion of the main theorem to clarify that the results benchmark behavior when stability can be assessed from data, while preserving generality for the fully open case. revision: partial

Circularity Check

0 steps flagged

No significant circularity; new definitions support independent regret analysis

full rationale

The paper defines pre-training degree, stability, and global dynamic regret as new quantities to capture open-system complexities, then derives global-UCB regret bounds and matching lower bounds in terms of these quantities. This constitutes standard modeling followed by analysis rather than any reduction of the claimed results to the inputs by construction. No self-citations, fitted parameters renamed as predictions, or ansatzes smuggled via prior work appear in the provided text; the derivation chain remains self-contained against the introduced model.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 3 invented entities

Based on abstract only; paper introduces new concepts as foundational but no explicit free parameters, standard axioms, or prior citations are detailed. New entities are postulated to capture open-system complexities.

invented entities (3)

pre-training degree no independent evidence
purpose: Quantifies information carried by newly arriving agents
Newly defined to capture endogenous non-stationarity from agent arrivals.
stability no independent evidence
purpose: Measures impact of new agents on overall system dynamics
Introduced to classify regimes where regret behaves differently.
global dynamic regret no independent evidence
purpose: Compares cumulative reward of active agents against varying optimal arms
New regret notion tailored to open multi-agent setting.

pith-pipeline@v0.9.0 · 5515 in / 1216 out tokens · 23281 ms · 2026-05-08T13:27:20.992119+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

253 extracted references · 6 canonical work pages

[1]

2025 IEEE Symposium on Security and Privacy (SP) , pages=

Permissionless verifiable information dispersal (data availability for bitcoin rollups) , author=. 2025 IEEE Symposium on Security and Privacy (SP) , pages=. 2025 , organization=

2025
[2]

ACM Computing Surveys , volume=

On identity, transaction, and smart contract privacy on permissioned and permissionless blockchain: a comprehensive survey , author=. ACM Computing Surveys , volume=. 2024 , publisher=

2024
[3]

2019 IEEE Symposium on Security and Privacy (SP) , pages=

Redactable blockchain in the permissionless setting , author=. 2019 IEEE Symposium on Security and Privacy (SP) , pages=. 2019 , organization=

2019
[4]

2019 IEEE 23rd International Enterprise Distributed Object Computing Conference (EDOC) , pages=

Process-based composition of permissioned and permissionless blockchain smart contracts , author=. 2019 IEEE 23rd International Enterprise Distributed Object Computing Conference (EDOC) , pages=. 2019 , organization=

2019
[5]

World Wide Web , volume=

Distributed attribute-based access control system using permissioned blockchain , author=. World Wide Web , volume=. 2021 , publisher=

2021
[6]

2018 IEEE international conference on engineering, technology and innovation (ICE/ITMC) , pages=

CredenceLedger: a permissioned blockchain for verifiable academic credentials , author=. 2018 IEEE international conference on engineering, technology and innovation (ICE/ITMC) , pages=. 2018 , organization=

2018
[7]

2019 IEEE 39th International Conference on Distributed Computing Systems (ICDCS) , pages=

Parblockchain: Leveraging transaction parallelism in permissioned blockchain systems , author=. 2019 IEEE 39th International Conference on Distributed Computing Systems (ICDCS) , pages=. 2019 , organization=

2019
[8]

Management Science , volume=

Economics of permissioned blockchain adoption , author=. Management Science , volume=. 2023 , publisher=

2023
[9]

Stochastic processes and their Applications , volume=

Poisson convergence and Poisson processes with applications to random graphs , author=. Stochastic processes and their Applications , volume=. 1987 , publisher=

1987
[10]

Journal of Applied Probability , volume=

Stein's method and Poisson process convergence , author=. Journal of Applied Probability , volume=. 1988 , publisher=

1988
[11]

Wiley Encyclopedia of Operations Research and Management Science , year=

Generating homogeneous Poisson processes , author=. Wiley Encyclopedia of Operations Research and Management Science , year=
[12]

Journal of Applied Probability , volume=

A characterization of the Poisson process , author=. Journal of Applied Probability , volume=. 1974 , publisher=

1974
[13]

Mathematics of Operations Research , volume=

Online Markov decision processes , author=. Mathematics of Operations Research , volume=. 2009 , publisher=

2009
[14]

Mathematics of Operations Research , volume=

Robust Markov decision processes , author=. Mathematics of Operations Research , volume=. 2013 , publisher=

2013
[15]

Journal of mathematics and mechanics , pages=

A Markovian decision process , author=. Journal of mathematics and mechanics , pages=. 1957 , publisher=

1957
[16]

Proceedings of the ACM on Measurement and Analysis of Computer Systems , year=

Heterogeneous Multi-agent Multi-armed Bandits on Stochastic Block Models , author=. Proceedings of the ACM on Measurement and Analysis of Computer Systems , year=
[17]

Proceedings of the ACM on Measurement and Analysis of Computing Systems , volume=

Robust multi-agent bandits over undirected graphs , author=. Proceedings of the ACM on Measurement and Analysis of Computing Systems , volume=. 2022 , publisher=

2022
[18]

arXiv preprint arXiv:2310.07320 , year=

Byzantine-resilient decentralized multi-armed bandits , author=. arXiv preprint arXiv:2310.07320 , year=

work page arXiv
[19]

Proceedings of the Twenty-second International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks and Mobile Computing , pages=

Robust multi-agent multi-armed bandits , author=. Proceedings of the Twenty-second International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks and Mobile Computing , pages=
[20]

The Annals of Probability , pages=

On the convergence of Poisson binomial to Poisson distributions , author=. The Annals of Probability , pages=. 1974 , publisher=

1974
[21]

2019 International Conference on Information and Communication Technology Convergence (ICTC) , pages=

A scalable semi-permissionless blockchain framework , author=. 2019 International Conference on Information and Communication Technology Convergence (ICTC) , pages=. 2019 , organization=

2019
[22]

IEEE Transactions on Information Forensics and Security , volume=

Wolverine: A scalable and transaction-consistent redactable permissionless blockchain , author=. IEEE Transactions on Information Forensics and Security , volume=. 2023 , publisher=

2023
[23]

ACM Computing Surveys , volume=

Performance modeling of public permissionless blockchains: A survey , author=. ACM Computing Surveys , volume=. 2025 , publisher=

2025
[24]

International Journal of Information Management , volume=

Permissionless and permissioned blockchain diffusion , author=. International Journal of Information Management , volume=. 2020 , publisher=

2020
[25]

2017 , publisher=

The theory of stochastic processes , author=. 2017 , publisher=

2017
[26]

2013 , publisher=

Introduction to stochastic processes , author=. 2013 , publisher=

2013
[27]

Operations Research , volume=

Approximate queuing models for multiprogramming computer systems , author=. Operations Research , volume=. 1973 , publisher=

1973
[28]

Transportation Science , volume=

A queuing model of the airport departure process , author=. Transportation Science , volume=. 2016 , publisher=

2016
[29]

Proceedings of the ACM on Measurement and Analysis of Computing Systems , volume=

Social learning in multi agent multi armed bandits , author=. Proceedings of the ACM on Measurement and Analysis of Computing Systems , volume=. 2019 , publisher=

2019
[30]

IEEE Journal on Selected Areas in Communications , volume=

Privacy-preserving communication-efficient federated multi-armed bandits , author=. IEEE Journal on Selected Areas in Communications , volume=. 2022 , publisher=

2022
[31]

International Conference on Artificial Intelligence and Statistics , pages=

Optimal algorithms for multiplayer multi-armed bandits , author=. International Conference on Artificial Intelligence and Statistics , pages=. 2020 , organization=

2020
[32]

The Eleventh International Conference on Learning Representations , year=

Achieving Near-Optimal Individual Regret & Low Communications in Multi-Agent Bandits , author=. The Eleventh International Conference on Learning Representations , year=
[33]

The 28th International Conference on Artificial Intelligence and Statistics , year=

Multi-agent Multi-armed Bandit Regret Complexity and Optimality , author=. The 28th International Conference on Artificial Intelligence and Statistics , year=
[34]

ICASSP 2024-2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) , pages=

Distributed stochastic contextual bandits for protein drug interaction , author=. ICASSP 2024-2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) , pages=. 2024 , organization=

2024
[35]

Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V

Biological pathway guided gene selection through collaborative reinforcement learning , author=. Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V. 2 , pages=
[36]

Proceedings of the 2018 World Wide Web Conference , pages=

Learning to collaborate: Multi-scenario ranking via multi-agent reinforcement learning , author=. Proceedings of the 2018 World Wide Web Conference , pages=

2018
[37]

Journal of Machine Learning Research , volume=

Multi-agent multi-armed bandits with limited communication , author=. Journal of Machine Learning Research , volume=
[38]

IEEE Transactions on Cognitive Communications and Networking , volume=

Multi-agent reinforcement learning-based joint caching and routing in heterogeneous networks , author=. IEEE Transactions on Cognitive Communications and Networking , volume=. 2024 , publisher=

2024
[39]

IEEE Transactions on Wireless Communications , volume=

Multi-connection based scalable video streaming in UDNs: A multi-agent multi-armed bandit approach , author=. IEEE Transactions on Wireless Communications , volume=. 2021 , publisher=

2021
[40]

Advances in Neural Information Processing Systems , volume=

A decision-language model (dlm) for dynamic restless multi-armed bandit tasks in public health , author=. Advances in Neural Information Processing Systems , volume=
[41]

Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining , pages=

A tutorial on multi-armed bandit applications for large language models , author=. Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining , pages=
[42]

Advances in Neural Information Processing Systems , volume=

Collapsing bandits and their application to public health intervention , author=. Advances in Neural Information Processing Systems , volume=
[43]

Information Systems Research , volume=

Spoiled for choice? Personalized recommendation for healthcare decisions: A multiarmed bandit approach , author=. Information Systems Research , volume=. 2023 , publisher=

2023
[44]

Proceedings of the 32nd ACM International Conference on Information and Knowledge Management , pages=

Scalable neural contextual bandit for recommender systems , author=. Proceedings of the 32nd ACM International Conference on Information and Knowledge Management , pages=
[45]

Proceedings of the 14th ACM Conference on Recommender Systems , pages=

Introduction to bandits in recommender systems , author=. Proceedings of the 14th ACM Conference on Recommender Systems , pages=
[46]

Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining , pages=

Multi-armed bandits and reinforcement learning: Advancing decision making in e-commerce and beyond , author=. Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining , pages=
[47]

a/b tests in e-commerce-confidence interval and hypothesis test power perspectives , author=

Multi armed bandit vs. a/b tests in e-commerce-confidence interval and hypothesis test power perspectives , author=. Proceedings of the 28th ACM SIGKDD conference on knowledge discovery and data mining , pages=
[48]

Conference on Learning Theory , pages=

Bounded regret in stochastic multi-armed bandits , author=. Conference on Learning Theory , pages=. 2013 , organization=

2013
[49]

Multi-agent Multi-armed Bandit Regret Complexity and Optimality , author=
[50]

ACM Computing Surveys , volume=

On identity, transaction, and smart contract privacy on permissioned and permissionless blockchain: A comprehensive survey , author=. ACM Computing Surveys , volume=. 2024 , publisher=

2024
[51]

Lewis-Pye and T

Permissionless consensus , author=. arXiv preprint arXiv:2304.14701 , year=

work page arXiv
[52]

Advances in applied mathematics , volume=

Asymptotically efficient adaptive allocation rules , author=. Advances in applied mathematics , volume=. 1985 , publisher=

1985
[53]

Coordination and Cooperation in Multi-Agent Reinforcement Learning (Honorable Mention) , year=

Decentralized Blockchain-based Robust Multi-agent Multi-armed Bandit , author=. Coordination and Cooperation in Multi-Agent Reinforcement Learning (Honorable Mention) , year=
[54]

IEEE Control Systems Letters , volume=

Cooperative learning for adversarial multi-armed bandit on open multi-agent systems , author=. IEEE Control Systems Letters , volume=. 2023 , publisher=

2023
[55]

, author =

DORA the explorer: directed outreaching reinforcement action-selection. , author =
[56]

, author =

Adaptive -greedy exploration in reinforcement learning based on value differences. , author =. Annual Conference on Artificial Intelligence , pages =
[57]

, author =

An adaptive greedy algorithm with application to nonlinear communications. , author =. IEEE Transactions on Signal Processing , publisher =
[58]

, author =

An adaptive implementation of -Greedy in reinforcement Learning. , author =. Procedia Computer Science , publisher =
[59]

, author =

An analysis of model-based interval estimation for Markov decision processes. , author =. Journal of Computer and System Sciences , publisher =
[60]

, author =

Unifying count-based exploration and intrinsic motivation. , author =. Advances in Neural Information Processing Systems , pages =
[61]

, author =

Deep exploration via bootstrapped DQN. , author =. Advances in Neural Information Processing Systems , pages =
[62]

, author =

An empirical evaluation of thompson sampling. , author =. Advances in neural information processing systems , pages =
[63]

, author =

Randomized prior functions for deep reinforcement learning. , author =. Advances in Neural Information Processing Systems , pages =
[64]

, author =

Deep reinforcement learning with double q-learning. , author =
[65]

, author =

Incentivizing exploration in reinforcement learning with deep predictive models. , author =
[66]

, author =

Go-explore: a new approach for hard-exploration problems. , author =
[67]

, author =

The nonstochastic multiarmed bandit problem. , author =. SIAM Journal on Computing , publisher =
[68]

Machine Learning , publisher =

Finite-time analysis of the multiarmed bandit problem , author =. Machine Learning , publisher =
[69]

, author =

On the likelihood that one unknown probability exceeds another in view of the evidence of two samples. , author =. Biometrika , publisher =
[70]

, author =

Contextual bandit algorithms with supervised learning guarantees. , author =. Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics , pages =
[71]

, author =

Exploration by random network distillation. , author =
[72]

, author =

Playing Atari with deep reinforcement learning. , author =
[73]

, author =

Proximal policy optimization algorithms. , author =
[74]

, author =

Regret analysis of stochastic and nonstochastic multi-armed bandit Problems. , author =
[75]

, author =

Improving the expected improvement algorithm. , author =. Advances in Neural Information Processing Systems , pages =
[76]

, author =

Gaussian process optimization in the bandit setting: no regret and experimental design. , author =
[77]

, author =

Ensemble of feature sets and classification algorithms for sentiment classification. , author =. Information Sciences , publisher =
[78]

, author =

Efficient global optimization of expensive black-box functions. , author =. Journal of Global optimization , publisher =
[79]

, author =

Human-level control through deep reinforcement learning. , author =. Nature , publisher =
[80]

8803 Machine learning theory , author =

Showing first 80 references.