A Computationally Efficient FPTAS for Convex Stochastic Dynamic Programs

Abstract

We propose a computationally efficient Fully Polynomial-Time Approximation Scheme (FPTAS) for convex stochastic dynamic programs using the technique of K-approximation sets and functions introduced by Halman et al. This paper deals with the convex case only, and it has the following contributions: First, we improve on the worst-case running time given by Halman et al. Second, we design an FPTAS with excellent computational performance, and show that it is faster than an exact algorithm even for small problem instances and small approximation factors, becoming orders of magnitude faster as the problem size increases. Third, we show that with careful algorithm design, the errors introduced by floating point computations can be bounded, so that we can provide a guarantee on the approximation factor over an exact infinite-precision solution. Our computational evaluation is based on randomly generated problem instances coming from applications in supply chain management and finance.