OSPHG algorithm achieves sub-linear (1-1/e)-regret and sub-linear budget violation for online DR-submodular maximization with long-term budgets when W = o(T).
Trading regret for efficiency: online convex optimization with long term constraints
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Online Continuous DR-Submodular Maximization with Long-Term Budget Constraints
OSPHG algorithm achieves sub-linear (1-1/e)-regret and sub-linear budget violation for online DR-submodular maximization with long-term budgets when W = o(T).