Online Risk-Averse Submodular Maximization

TL;DR

This paper introduces a polynomial-time online algorithm for maximizing CVaR of stochastic submodular functions, achieving near-optimal solutions with reduced space complexity and practical effectiveness in portfolio optimization.

Contribution

It presents the first online algorithm for CVaR maximization of monotone stochastic submodular functions with convergence guarantees and lower space requirements.

Findings

Converges to a (1-1/e)-approximate solution at rate O(T^{-1/4})

Requires only O(√T) space compared to previous Ω(T) space algorithms

Performs well in real-world portfolio optimization tasks

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 $\Omega(T)$ space, our online algorithm only requires $O(\sqrt{T})$ 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.