Logarithmic Regret for Unconstrained Submodular Maximization Stochastic Bandit

• URL: http://arxiv.org/abs/2410.08578v2
• Date: Wed, 12 Feb 2025 09:50:05 GMT
• Title: Logarithmic Regret for Unconstrained Submodular Maximization Stochastic Bandit
• Authors: Julien Zhou, Pierre Gaillard, Thibaud Rahier, Julyan Arbel,
• Abstract summary: We address the online un submodular problem (Online USM) in a setting with bandit feedback.<n>In this framework, a-maker receives noisy rewards from a monotone submodular function taking values in a known interval.<n>We introduce a problem-dependent notion of hardness characterizing the transition between logarithmic and regime for the upper bounds.
• Score: 12.096516329746292
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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