Randomized algorithms
The Sample Average Approximation Method for Stochastic Discrete Optimization
SIAM Journal on Optimization
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Boosted sampling: approximation algorithms for stochastic optimization
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
An Edge in Time Saves Nine: LP Rounding Approximation Algorithms for Stochastic Network Design
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Stochastic Optimization is (Almost) as easy as Deterministic Optimization
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Facility location and the analysis of algorithms through factor-revealing programs
Facility location and the analysis of algorithms through factor-revealing programs
On the random 2-stage minimum spanning tree
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On two-stage stochastic minimum spanning trees
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Sampling-based Approximation Algorithms for Multi-stage Stochastic
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Provably near-optimal sampling-based algorithms for Stochastic inventory control models
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Approximation algorithms for budgeted learning problems
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximation algorithms for stochastic and risk-averse optimization
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Stochastic analyses for online combinatorial optimization problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A plant location guide for the unsure
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for 2-Stage Stochastic Scheduling Problems
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Infrastructure Leasing Problems
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Commitment under uncertainty: Two-stage stochastic matching problems
Theoretical Computer Science
Stochastic Steiner Tree with Non-uniform Inflation
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
The ratio index for budgeted learning, with applications
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A constant-factor approximation for stochastic Steiner forest
Proceedings of the forty-first annual ACM symposium on Theory of computing
Stochastic Combinatorial Optimization with Controllable Risk Aversion Level
Mathematics of Operations Research
A Plant Location Guide for the Unsure: Approximation Algorithms for Min-Max Location Problems
Mathematics of Operations Research
Stochastic models for budget optimization in search-based advertising
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Optimal online assignment with forecasts
Proceedings of the 11th ACM conference on Electronic commerce
Correlation robust stochastic optimization
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Sampling and Cost-Sharing: Approximation Algorithms for Stochastic Optimization Problems
SIAM Journal on Computing
Approximation algorithms for 2-stage stochastic optimization problems
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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
Price of Correlations in Stochastic Optimization
Operations Research
Stochastic vehicle routing with recourse
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Commitment under uncertainty: two-stage stochastic matching problems
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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A large class of stochastic optimization problems can be modeled as minimizing an objective function f that depends on a choice of a vector x ∈ X, as well as on a random external parameter ω∈ Ω given by a probability distribution π. The value of the objective function is a random variable and often the goal is to find an x ∈ X to minimize the expected cost Eω[fω(x)]. Each ω is referred to as a scenario. We consider the case when Ω is large or infinite and we are allowed to sample from π in a black-box fashion. A common method, known as the SAA method (sample average approximation), is to pick sufficiently many independent samples from π and use them to approximate π and correspondingly Eω[fω(x)]. This is one of several scenario reduction methods used in practice. There has been substantial recent interest in two-stage stochastic versions of combinatorial optimization problems which can be modeled by the framework described above. In particular, we are interested in the model where a parameter λ bounds the relative factor by which costs increase if decisions are delayed to the second stage. Although the SAA method has been widely analyzed, the known bounds on the number of samples required for a (1+ε) approximation depend on the variance of π even when λ is assumed to be a fixed constant. Shmoys and Swamy [13,14] proved that a polynomial number of samples suffice when f can be modeled as a linear or convex program. They used modifications to the ellipsoid method to prove this. In this paper we give a different proof, based on earlier methods of Kleywegt, Shapiro, Homem-De-Mello [6] and others, that a polynomial number of samples suffice for the SAA method. Our proof is not based on computational properties of f and hence also applies to integer programs. We further show that small variations of the SAA method suffice to obtain a bound on the sample size even when we have only an approximation algorithm to solve the sampled problem. We are thus able to extend a number of algorithms designed for the case when π is given explicitly to the case when π is given as a black-box sampling oracle.