Online risk-averse submodular maximization

Abstract

AbstractWe 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.