Approximation algorithms for facility location problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
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The Sample Average Approximation Method for Stochastic Discrete Optimization
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Boosted sampling: approximation algorithms for stochastic optimization
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Sampling-based Approximation Algorithms for Multi-stage Stochastic
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
How to Pay, Come What May: Approximation Algorithms for Demand-Robust Covering Problems
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Hedging Uncertainty: Approximation Algorithms for Stochastic Optimization Problems
Mathematical Programming: Series A and B
LP Rounding Approximation Algorithms for Stochastic Network Design
Mathematics of Operations Research
Sampling bounds for stochastic optimization
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Stochastic combinatorial optimization with controllable risk aversion level
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Low order-value approach for solving VaR-constrained optimization problems
Journal of Global Optimization
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Most of the recent work on 2-stage stochastic combinatorial optimization problems has focused on minimization of the expected cost or the worst-case cost of the solution. Those two objectives can be viewed as two extreme ways of handling risk. In this paper we propose to use a one-parameter family of functionals to interpolate between them. Although such a family has been used in the mathematical finance and stochastic programming literature before, its use in the context of approximation algorithms seems new. We show that under standard assumptions, a broad class of risk-adjusted 2-stage stochastic programs can be efficiently treated by the sample average approximation (SAA) method. In particular, our result shows that it is computationally feasible to incorporate some degree of robustness even when the underlying distribution can only be accessed in a black-box fashion. We also show that when combined with suitable rounding procedures, our result yields new approximation algorithms for many risk-adjusted 2-stage stochastic combinatorial optimization problems under the black-box setting.