Logarithmic Sample Bounds For Sample Average Approximation With Capacity- Or Budget-Constraints

Sample Average Approximation (SAA) is used to approximately solve stochastic optimization problems. In practice, SAA requires much fewer samples than predicted by existing theoretical bounds that ensure the SAA solution is close to optimal. Here, we derive new sample-size bounds for SAA that, for certain problems, are logarithmic (existing bounds are polynomial) in problem dimension. Notably, our new bounds provide a theoretical explanation for the success of SAA for many capacity- or budget-constrained optimization problems. (C) 2021 Elsevier B.V. All rights reserved.