Parallel and distributed computing for stochastic dual dynamic programming

Abstract

We study different parallelization schemes for the stochastic dual dynamic programming (SDDP) algorithm. We propose a taxonomy for these parallel algorithms, which is based on the concept of parallelizing by scenario and parallelizing by node of the underlying stochastic process. We develop a synchronous and asynchronous version for each configuration. The parallelization strategy in the parallelscenario configuration aims at parallelizing the Monte Carlo sampling procedure in the forward pass of the SDDP algorithm, and thus generates a large number of supporting hyperplanes in parallel. On the other hand, the parallel-node strategy aims at building a single hyperplane of the dynamic programming value function in parallel. The considered algorithms are implemented using Julia and JuMP on a high performance computing cluster. We study the effectiveness of the methods in terms of achieving tight optimality gaps, as well as the scalability properties of the algorithms with respect to an increasing number of CPUs. In particular, we study the effects of the different parallelization strategies on performance when increasing the number of Monte Carlo samples in the forward pass, and demonstrate through numerical experiments that such an increase may be harmful. Our results indicate that a parallel-node strategy presents certain benefits as compared to a parallel-scenario configuration.