Communication-Corruption Coupling and Verification in Cooperative Multi-Objective Bandits
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arXiv
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| Format: | Preprint |
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2026
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| author | Shi, Ming |
| author_facet | Shi, Ming |
| contents | We study cooperative stochastic multi-armed bandits with vector-valued rewards under adversarial corruption and limited verification. In each of $T$ rounds, each of $N$ agents selects an arm, the environment generates a clean reward vector, and an adversary perturbs the observed feedback subject to a global corruption budget $Γ$. Performance is measured by team regret under a coordinate-wise nondecreasing, $L$-Lipschitz scalarization $ϕ$, covering linear, Chebyshev, and smooth monotone utilities. Our main contribution is a communication-corruption coupling: we show that a fixed environment-side budget $Γ$ can translate into an effective corruption level ranging from $Γ$ to $NΓ$, depending on whether agents share raw samples, sufficient statistics, or only arm recommendations. We formalize this via a protocol-induced multiplicity functional and prove regret bounds parameterized by the resulting effective corruption. As corollaries, raw-sample sharing can suffer an $N$-fold larger additive corruption penalty, whereas summary sharing and recommendation-only sharing preserve an unamplified $O(Γ)$ term and achieve centralized-rate team regret. We further establish information-theoretic limits, including an unavoidable additive $Ω(Γ)$ penalty and a high-corruption regime $Γ=Θ(NT)$ where sublinear regret is impossible without clean information. Finally, we characterize how a global budget $ν$ of verified observations restores learnability. That is, verification is necessary in the high-corruption regime, and sufficient once it crosses the identification threshold, with certified sharing enabling the team's regret to become independent of $Γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11924 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Communication-Corruption Coupling and Verification in Cooperative Multi-Objective Bandits Shi, Ming Machine Learning We study cooperative stochastic multi-armed bandits with vector-valued rewards under adversarial corruption and limited verification. In each of $T$ rounds, each of $N$ agents selects an arm, the environment generates a clean reward vector, and an adversary perturbs the observed feedback subject to a global corruption budget $Γ$. Performance is measured by team regret under a coordinate-wise nondecreasing, $L$-Lipschitz scalarization $ϕ$, covering linear, Chebyshev, and smooth monotone utilities. Our main contribution is a communication-corruption coupling: we show that a fixed environment-side budget $Γ$ can translate into an effective corruption level ranging from $Γ$ to $NΓ$, depending on whether agents share raw samples, sufficient statistics, or only arm recommendations. We formalize this via a protocol-induced multiplicity functional and prove regret bounds parameterized by the resulting effective corruption. As corollaries, raw-sample sharing can suffer an $N$-fold larger additive corruption penalty, whereas summary sharing and recommendation-only sharing preserve an unamplified $O(Γ)$ term and achieve centralized-rate team regret. We further establish information-theoretic limits, including an unavoidable additive $Ω(Γ)$ penalty and a high-corruption regime $Γ=Θ(NT)$ where sublinear regret is impossible without clean information. Finally, we characterize how a global budget $ν$ of verified observations restores learnability. That is, verification is necessary in the high-corruption regime, and sufficient once it crosses the identification threshold, with certified sharing enabling the team's regret to become independent of $Γ$. |
| title | Communication-Corruption Coupling and Verification in Cooperative Multi-Objective Bandits |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2601.11924 |