Online risk-averse submodular maximization
Name
10479_2022_Article_4835.pdf
Size
640.74 KB
Format
Adobe PDF
Checksum (MD5)
a6d48d0961bcc8d1a877b4334e187b03
Author(s)
Soma, Tasuku
Yoshida, Yuichi
Date Issued
August 25, 2022
Publisher
Springer US
Citation
Soma, Tasuku and Yoshida, Yuichi. 2022. "Online risk-averse submodular maximization."
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10479-022-04835-9
