Approximation algorithms for stochastic and risk-averse optimization

TL;DR

This paper develops improved approximation algorithms for multi-stage stochastic and risk-averse optimization problems, matching non-stochastic performance and advancing solutions for facility location and covering problems.

Contribution

It introduces algorithms with better approximation ratios for stochastic covering, facility location, and multi-stage problems, surpassing previous bounds and extending to general distribution models.

Findings

Multi-stage covering problems admit similar approximations as non-stochastic versions.

New algorithms achieve a 2.2975-approximation for stochastic facility location.

Enhanced guarantees for risk-averse and black-box distribution models.

Abstract

We present improved approximation algorithms in stochastic optimization. We prove that the multi-stage stochastic versions of covering integer programs (such as set cover and vertex cover) admit essentially the same approximation algorithms as their standard (non-stochastic) counterparts; this improves upon work of Swamy \& Shmoys which shows an approximability that depends multiplicatively on the number of stages. We also present approximation algorithms for facility location and some of its variants in the $2$-stage recourse model, improving on previous approximation guarantees. We give a $2.2975$-approximation algorithm in the standard polynomial-scenario model and an algorithm with an expected per-scenario $2.4957$-approximation guarantee, which is applicable to the more general black-box distribution model.