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arXiv · 2105.09838

Online Risk-Averse Submodular Maximization

Tasuku Soma·Yuichi Yoshida
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Abstract

We present a polynomial-time online algorithm for maximizing the conditional value at risk (CVaR) of a monotone stochastic submodular function. Given $T$ i.i.d. samples from an underlying distribution arriving online, our algorithm produces a sequence of solutions that converges to a ($1-1/e$)-approximate solution with a convergence rate of $O(T^{-1/4})$ for monotone continuous DR-submodular functions. Compared with previous offline algorithms, which require $Ω(T)$ space, our online algorithm only requires $O(\sqrt{T})$ space. We extend our online algorithm to portfolio optimization for monotone submodular set functions under a matroid constraint. Experiments conducted on real-world datasets demonstrate that our algorithm can rapidly achieve CVaRs that are comparable to those obtained by existing offline algorithms.

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Tasuku Soma, Yuichi Yoshida. 2021-05-20. Online Risk-Averse Submodular Maximization. https://arxiv.org/abs/2105.09838

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