A note on sample complexity of multistage stochastic programs
نویسنده
چکیده
We derive a lower bound for the sample complexity of the Sample Average Approximation method for a certain class of multistage stochastic optimization problems. In previous works, upper bounds for such problems were derived. We show that the dependence of the lower bound with respect to the complexity parameters and the problem's data are comparable to the upper bound's estimates. Like previous results, our lower bound presents an additional multiplicative factor showing that it is unavoidable for certain stochastic problems.
منابع مشابه
A note on complexity of multistage stochastic programs
In Shapiro [2006], estimates of the sample sizes required to solve a multistage stochastic programming problem with a given accuracy by the conditional sample average approximation method were derived. In this paper we construct an example in the multistage setting that shows that these estimates cannot be significantly improved.
متن کاملRevisiting some results on the sample complexity of multistage stochastic programs and some extensions
In this work we present explicit definitions for the sample complexity associated with the Sample Average Approximation (SAA) Method for instances and classes of multistage stochastic optimization problems. For such, we follow the same notion firstly considered in Kleywegt et al. (2001). We define the sample complexity for an arbitrary class of problems by considering its worst case behavior, a...
متن کاملAn Interior Random Vector Algorithm for MultiStage Stochastic Linear Programs
In this paper, an interior point algorithm for linear programs is adapted for solving multistage stochastic linear programs. The algorithm is based on Monteiro and Adler’s path-following algorithm for deterministic linear programs. In practice, the complexity of the algorithm is linear with respect to the size of the sample space. The algorithm starts from a feasible solution of the problem and...
متن کاملOn complexity of multistage stochastic programs
In this paper we derive estimates of the sample sizes required to solve a multistage stochastic programming problem with a given accuracy by the (conditional sampling) sample average approximation method. The presented analysis is self contained and is based on a, relatively elementary, one dimensional Cramér’s Large Deviations Theorem.
متن کاملRevisiting some results on the complexity of multistage stochastic programs and some extensions
In this work we present explicit definitions for the sample complexity associated with the Sample Average Approximation (SAA) Method for instances and classes of multistage stochastic optimization problems. For such, we follow the same notion firstly considered in Kleywegt et al. (2001). We define the complexity for an arbitrary class of problems by considering its worst case behavior, as it is...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Oper. Res. Lett.
دوره 44 شماره
صفحات -
تاریخ انتشار 2016