Online risk-averse submodular maximization

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(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.