Algorithms for Probabilistically-Constrained Models of Risk-Averse Stochastic Optimization with Black-Box Distributions

Details Algorithms for Probabilistically-Constrained Models of Risk-Averse Stochastic Optimization with Black-Box Distributions Algorithms for Probabilistically-Constrained Models of Risk-Averse Stochastic Optimization with Black-Box Distributions

2008-05-04

arxiv.org/abs/0805.0389v1

Computer Science

Data Structures and Algorithms

Scientific paper

We consider various stochastic models that incorporate the notion of risk-averseness into the standard 2-stage recourse model, and develop novel techniques for solving the algorithmic problems arising in these models. A key notable feature of our work that distinguishes it from work in some other related models, such as the (standard) budget model and the (demand-) robust model, is that we obtain results in the black-box setting, that is, where one is given only sampling access to the underlying distribution. Our first model, which we call the risk-averse budget model, incorporates the notion of risk-averseness via a probabilistic constraint that restricts the probability (according to the underlying distribution) with which the second-stage cost may exceed a given budget B to at most a given input threshold \rho. We also a consider a closely-related model that we call the risk-averse robust model, where we seek to minimize the first-stage cost and the (1-\rho)-quantile of the second-stage cost. We obtain approximation algorithms for a variety of combinatorial optimization problems including the set cover, vertex cover, multicut on trees, min cut, and facility location problems, in the risk-averse budget and robust models with black-box distributions. We obtain near-optimal solutions that preserve the budget approximately and incur a small blow-up of the probability threshold (both of which are unavoidable). To the best of our knowledge, these are the first approximation results for problems involving probabilistic constraints and black-box distributions. A major component of our results is a fully polynomial approximation scheme for solving the LP-relaxation of the risk-averse problem.

Affiliated with

Also associated with

No associations

Rating

Algorithms for Probabilistically-Constrained Models of Risk-Averse Stochastic Optimization with Black-Box Distributions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Algorithms for Probabilistically-Constrained Models of Risk-Averse Stochastic Optimization with Black-Box Distributions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Algorithms for Probabilistically-Constrained Models of Risk-Averse Stochastic Optimization with Black-Box Distributions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-324644