Communication Dans Un Congrès Année : 2025

Logarithmic Regret for Unconstrained Submodular Maximization Stochastic Bandit

Résumé

We address the online unconstrained submodular maximization problem (Online USM), in a setting with stochastic bandit feedback. In this framework, a decision-maker receives noisy rewards from a non monotone submodular function taking values in a known bounded interval. This paper proposes Double-Greedy - Explore-then-Commit (DG-ETC), adapting the Double-Greedy approach from the offline and online full-information settings. DG-ETC satisfies a O(d log(dT)) problem-dependent upper bound for the 1/2-approximate pseudo-regret, as well as a O(dT^{2/3} log(dT)^{1/3}) problem-free one at the same time, outperforming existing approaches. In particular, we introduce a problem-dependent notion of hardness characterizing the transition between logarithmic and polynomial regime for the upper bounds.
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Dates et versions

hal-04729023 , version 1 (10-10-2024)
hal-04729023 , version 2 (10-02-2025)

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Julien Zhou, Pierre Gaillard, Thibaud Rahier, Julyan Arbel. Logarithmic Regret for Unconstrained Submodular Maximization Stochastic Bandit. ALT 2025 - 36th International Conference on Algorithmic Learning Theory, Feb 2025, Milan, Italy. pp.1-25, ⟨10.48550/arXiv.2410.08578⟩. ⟨hal-04729023v2⟩
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