Competitive Algorithms for Online Budget-Constrained Continuous DR-Submodular Problems
This work addresses online optimization with non-concave functions for applications like resource allocation, but it is incremental as it extends known bounds to a broader class.
The paper tackled the problem of online optimization for maximizing monotone DR-submodular functions under budget constraints, achieving a competitive ratio that matches the known tight bound for linear objectives.
In this paper, we study a certain class of online optimization problems, where the goal is to maximize a function that is not necessarily concave and satisfies the Diminishing Returns (DR) property under budget constraints. We analyze a primal-dual algorithm, called the Generalized Sequential algorithm, and we obtain the first bound on the competitive ratio of online monotone DR-submodular function maximization subject to linear packing constraints which matches the known tight bound in the special case of linear objective function.