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- W2897861301 abstract "In this paper, we study the problem of monotone (weakly) DR-submodular continuous maximization. While previous methods require the gradient information of the objective function, we propose a derivative-free algorithm LDGM for the first time. We define $beta$ and $alpha$ to characterize how close a function is to continuous DR-submodulr and submodular, respectively. Under a convex polytope constraint, we prove that LDGM can achieve a $(1-e^{-beta}-epsilon)$-approximation guarantee after $O(1/epsilon)$ iterations, which is the same as the best previous gradient-based algorithm. Moreover, in some special cases, a variant of LDGM can achieve a $((alpha/2)(1-e^{-alpha})-epsilon)$-approximation guarantee for (weakly) submodular functions. We also compare LDGM with the gradient-based algorithm Frank-Wolfe under noise, and show that LDGM can be more robust. Empirical results on budget allocation verify the effectiveness of LDGM." @default.
- W2897861301 created "2018-10-26" @default.
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- W2897861301 date "2018-10-16" @default.
- W2897861301 modified "2023-09-23" @default.
- W2897861301 title "Maximizing Monotone DR-submodular Continuous Functions by Derivative-free Optimization" @default.
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- W2897861301 doi "https://doi.org/10.48550/arxiv.1810.06833" @default.
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