Online risk-averse submodular maximization

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