Online risk-averse submodular maximization

Tasuku Soma () and Yuichi Yoshida ()
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Tasuku Soma: Massachusetts Institute of Technology
Yuichi Yoshida: National Institute of Informatics

Annals of Operations Research, 2023, vol. 320, issue 1, No 15, 393-414

Abstract: 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 ( $$1-1/e$$ 1 - 1 / e )-approximate solution with a convergence rate of $$O(T^{-1/4})$$ O ( T - 1 / 4 ) for monotone continuous DR-submodular functions. Compared with previous offline algorithms, which require $$\Omega (T)$$ Ω ( T ) space, our online algorithm only requires $$O(\sqrt{T})$$ O ( 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.

Keywords: Conditional value at risk; Submodular function; Stochastic optimization; Online learning (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10479-022-04835-9

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